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UNIVERSITY   OF   CALIFORNIA 


LIBRARY 

OF  THE 

DEPARTMENT  OF  PHYStCS 


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LOWER  DIVISION 


ELEMENTARY  TREATISE 


ON 


NATURAL   PHILOSOPHY. 


BY 


A.  FRIVAT  DESCHANEL, 

FORMERLY  PROFESSOR  OF  PHYSICS   IN  THE  LTCEE  LOUIS-LE-GRAND, 
INSPECTOR  OF  THE  ACADEMY  OF  PARIS. 


TRANSLATED    AND    EDITED,    WITH    EXTENSIVE    ADDITIONS 

BY  J.  D.  EVERETT,  M.  A.,  D.  C.  L.,  F.  R.  S.  E., 

PKOFESSOB  OF  NATURAL  PHILOSOPHY  IN  THE   QUEEN'S  COLLEGE,   BELFAST. 

UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 
IN     FOUR     PA  RT  S. 


PART    II.  — HEAT. 

ILLUSTRATED  BY  ONE  HUNDRED   AND  FIFTY-ONE  ENGRAVINGS  ON   WOOD. 


NEW    YORK: 
D.    APPLETON    AND    COMPANY, 

1,  3,  AND    5    BOND    STREET. 

1881. 


PHYSICS  DEPT 


In  the  present  volume,  the  chapter  on  Thermo-dynamics  is  almost 
entirely  the  work  of  the  Editor.  Large  portions  of  the  chapters  on 
Conduction  and  on  Terrestrial  Temperatures  have  also  been  re- 
written; and  considerable  additions  have  been  made  in  connection 
with  Hygromebry,  the  Theory  of  Exchanges,  the  Specific  Heats  of 
Gases,  and  the  Motion  of  Glaciers.  Minor  additions  and  modifica- 
tions have  been  numerous,  and  will  easily  be  detected  by  comparison 
with  the  similarly  numbered  sections  in  the  original. 

The  nomenclature  of  units  of  heat  which  has  been  adopted,  is 
borrowed  from  Prof.  G.  C.  Foster's  article  "Heat"  in  Watts'  Dictionary 
of  Chemistry. 


CONTENTS-PAKT  II. 


HEAT. 

CHAPTER  XIX.    THERMOMETRY. 

Heat. — Cold. — Temperature. — Expansion  produced  by  heat. — Choice  of  thermometric 
substance. — Construction  of  mercurial  thermometer. — Fixed  points. — Thermometric 
scales.— Change  of  zero — Value  of  a  degree. — Sensibility. — Weight  thermometer. — 
Alcohol  thermometer.  —  Self-  registering  thermometers.  —  Six's.  —  Rutherford's.  — 
Phillips'. — Negretti's. — "Walferdin's. — Sea  and  well  thermometers. — Protection  against 
pressure  of  water. — Thermograph. — Metallic  thermometers. — Secchi's  meteorograph. 
— Pyrometers. — Differential  thermometers, pp.  241-263 

CHAPTER  XX.     FORMULA   RELATING  TO   EXPANSION. 

Expansion. — Expansion  factor. — Coefficient  of  expansion. — Cubic,  linear,  and  superficial 
expansion. — Comparison  of  volumes  and  densities  at  different  temperatures. — Correc- 
tion of  specific  gravity  for  temperature. — Gases, pp.  264-268. 

CHAPTER  XXI.     EXPANSION  OF  SOLIDS. 

Experiments  of  Laplace  and  Lavoisier. — Method  of  Ramsden  and  Roy. — Compensated 
pendulums. — Force  of  expansion  of  solids, pp.  269-274. 

CHAPTER  XXII.     EXPANSION  OF  LIQUIDS. 

Relation  between  apparent  and  absolute  expansion. — Expansion  of  glass. — Expansion  of 
any  liquid. — Maximum  density  of  water. — Saline  solutions. — Absolute  expansion  of 
mercury. — Expansion  of  iron  and  platinum. — Convection  of  heat  in  liquids. — Heating 
buildings  by  hot  water. —  Oceanic  currents, pp.  275-286. 

CHAPTER  XXIII.     EXPANSION   OF   GASES. 

Gay-Lussac's  experiments. — Regnault's  experiments. — Air-thermometer. — Absolute  tem- 
perature and  absolute  zero. — Regnault's  pyrometer. — Density  of  gases,  absolute  and 
relative. —  Experimental  determination. — Weight  of  a  litre  of  air. — Table  of  densities 
of  gases. — Draught  of  chimneys. — Stoves  and  fire-places,  ....  pp.  287-301. 

CHAPTER  XXIV.     FUSION   AND    SOLIDIFICATION. 

Fusion. — Table  of  melting-points. — Latent  heat. — Heat  of  fusion  of  ice. — Solution. — 
Freezing  mixtures. — Congelation. — Difficulty  of  making  a  commencement. — Cooling 
of  water  to  — 20°  C. — Crystallization. — Ice-flowers. — Supersaturation  and  sudden  con- 


VI  CONTENTS. 

gelation. — Change  of  volume  in  congelation. — Expansive  force  of  freezing  water. — 
Melting-point  raised  or  lowered  by  hydrostatic  pressure. — Effect  of  stress  in  solids 
upon  melting  and  solution. — Regelation. — Apparent  plasticity  of  ice. — Motion  of 
glaciers, pp.  302-316. 

CHAPTER  XXV.     EVAPOEATION  AND   CONDENSATION". 

Spontaneous  evaporation. — Vapours  and  permanent  gases. — Vapours  at  maximum  density 
and  tension,  or  saturated  vapours. — Maximum  density  and  tension  depend  on  tempera- 
ture.— Effect  of  presence  of  gas  or  of  another  vapour. — Dalton's  two  laws. — Liquefac- 
tion of  gases. — Faraday's  first  method. — Thilorier's  apparatus. — Bianchi's — Faraday's 
later  method. —  Continuous  transition  from  gas  to  liquid  or  from  liquid  to  gas. — Experi- 
ments of  Cagniard  de  la  Tour,  Drion,  and  Andrews. — Critical  temperature. — Latent 
heat  of  evaporation. — Cooling  by  evaporation. — Causing  water  to  freeze. — And  mer- 
cury.— Carry's  two  forms  of  apparatus  for  making  ice. — Cryophorus. — Solidification  of 
gases, pp.  317-333. 

CHAPTER  XXVI.     EBULLITION. 

Phenomena  of  ebullition. — Definite  temperature. — Constancy  of  temperature. — Tension  of 
Vapour. — Theory  of  ebullition. — Effect  of  pressure  on  boiling-point. — Franklin's  experi- 
ment.— Determination  of  heights  by  boiling-point. — Hypsometer. — Papin's  digester. — 
Safety-valve. — Boiling-point  of  saline  solutions. — Temperature  of  vapour  evolved. — 
Boiling-point  of  mixtures. — Difficulty  of  making  a  beginning  without  air. — Experi- 
ments of  Donny  and  Dufour. — Spheroidal  state. — Freezing  of  mercury  in  red-hot 
crucible. — Cause  of  the  spheroidal  state. — Distillation. — Conditions  of  rapid  evapora- 
tion,  pp.  334-348. 

CHAPTER  XXVII.     MEASUREMENT   OF   TENSION  AND 
DENSITY   OF   VAPOURS. 

Importance  in  connection  with  steam-engine. — Dalton's  experiments  on  maximum  tensions 
of  aqueous  vapour. — Regnault's  two  methods  of  experiment. — Table  of  results. — 
Representation  by  curve  and  empirical  formulae. — Vapours  of  other  liquids. — Expres- 
sion of  tensions  in  absolute  measure. — Laws  of  combination  by  volume. — Relation  of 
vapour  densities  (not  maximum)  to  chemical  equivalents. — Meaning  of  "  vapour- 
density"  of  a  substance. — Dumas'  method  of  determining  vapour-densities. — Example. 
— Table  of  vapour-densities. — Limiting  values  as  temperature  increases. — Gay-Lussac's 
method. — Volume  of  a  given  weight  of  steam, pp.  349-363. 

CHAPTER  XXVIII.     HYGROMETRY. 

Technical  meaning  of  "humidity." — Dew-point.  —  Hygroscopes.  —  Hygrometers. — De 
Saussnre's.  —  Dew-point  instruments.  —  Leroy's.  —  Daniell's.  —  Regnault's.  —  Wet  and 
dry  bulb. — Glaisher's  factors. — Apjohn's  formula,  and  discussion  of  the  basis  on  which 
it  rests. — Chemical  hygrometer. — Weight  of  given  volume  of  moist  air. — Volume  of 
saturated  air. — Aqueous  meteors. — Cloud  and  mist. — Supposed  vesicles. — Howard's 
nomenclature  of  clouds. — Causes  of  formation  of  cloud. — Rain. — Rain-gauge. — Annual 
rain-fall. — Snow  and  hail. — Snow-crystals, pp.  364-384. 

CHAPTER  XXIX.     RADIANT   HEAT. 

Radiation. — Characteristics  of. — Newton's  law  of  cooling. — Dulong  and  Petit's  law  of 
cooling. — Law  of  inverse  squares. — Experimental  proof. — Laws  of  reflection. — Burning- 


CONTENTS.  Vll 

mirrors. — Conjugate  mirrors. — Reflecting,  diffusive,  absorbing,  and  transmissive  powers. 
— Coefficients  of  emission  and  absorption  equal. — Absolute  value  of  coefficient  of 
radiation  for  lamp-black. — Different  kinds  of  heat-ray. — Theory  of  exchanges. — Ther- 
mopile.— Experimental  comparison  of  emissive  powers. — And  of  absorbing  powers. — 
Tables  of  results. — Variation  of  absorption  with  source  of  heat. — Determination  of  re- 
flecting powers. — And  diffusive  powers. — Diathermancy. — Experimental  measurement. 
— Table  of  heat  transmitted  by  different  substances. — Diathermancy  and  transparency. 
— Iodine  in  sulphide  of  carbon. — Rock-salt. — Diathermancy  of  gases. — Remarkable  effect 
of  scents  and  of  aqueous  vapour. — Influence  of  thickness  of  plate  upon  amount  of 
absorption. — Connection  between  radiant  heat  and  light. — Fluorescence  and  calor- 
escence. — Selective  emission  and  absorption. — Their  equality. — Proof  from  reversal  of 
bright  lines  in  spectrum, — Dew, pp.  385-413. 

CHAPTER  XXX.     CONDUCTION   OF   HEAT. 

Conduction  described  and  distinguished  from  radiation. — Variable  stage  and  permanent 
state. — Influence  of  specific  heat. — Definition  of  conductivity. — Mathematical  note  on 
conduction  during  variable  stage. — Experiments  to  illustrate  differences  of  conductivity. 
— Ingenhousz's  apparatus. — Metals  the  best  conductors. — Wire-gauze  and  Davy  lamp. 
— Domestic  applications. — Experimental  determination  of  conductivity. — Table  of 
results  obtained  by  Wiedemann  and  Franz, — Forbes'  determination  of  absolute  con- 
ductivity of  iron. — Absolute  conductivity  of  rock  deduced  from  underground  tempera- 
tures.— Conduction  in  liquids. — Despretz's  experiment  on  water. — Professor  Guthrie  on 
conducting  power  of  water. — Small  conducting  power  of  gases. — Accounts  for  warmth 
of  cloth,  &c. — Norwegian  cooking- box. — Conductivity  of  hydrogen,  .  pp.  414-425, 

CHAPTER  XXXI.     CALORIMETRY, 

Test  of  equal  quantity. — Units  of  heat,  gramme- degree,  pound-degree,  ,&c. — Thermal 
capacity,  or  water  equivalent. — Specific  heat,  or -capacity  per  unit  mass. — Capacity  per 
unit  volume. — Experiment  to  illustrate  differences  of  specific  <heat. — Measurement  of 
specific  heat  by  fusion  of  ice. — Method  of  mixtures. — Note  on  temperature  of  mixtures. 
— Calculation  of  experiment,  with  corrections. — Regnault's  apparatus. — Table  of  specific 
heats. — Great  specific  heat  of  water. — Effect  on  climate. — Dulong  and  Petit's  law. — 
Equal  thermal  capacities  of  all  atoms. — Specific  heat  of  gases,  at  constant  pressure,  and 
at  constant  temperature. — Their  laws. — Specific  heat  of  air. — Ratio  of  the  two  specific 
heats. — Changes  of  volume,  pressure,  and  temperature  when  no  heat  enters  or  escapes. — 
Latent  heat  of  fusion. — Table  of  latent  heats,  and  of  specific  heats  in  the  two  states. — 
Latent  heat  of  evaporation. — Despretz's  apparatus. — Regna/ult's  experiments. — Tables 
of  results. — Heat  of  chemical  combination. — Apparatus  of  Favre  and  Silbermann,  Dulong, 
Andrews. — Table  of  heats  of  combustion. — Oxy-hydrogen  blowpipe,  pp.  426-444. 

CHAPTER  XXXII.     THERMO-DYNAMICS. 

Connection  between  heat  and  work. — Caloric  theory.  Heat  developed  in  compression  and 
in  friction. — Rumford  experiments  on  the  boring  of  cannon. — Davy's  experiment  on 
friction  of  ice. — Recent  investigators. — Foucault's  electro- magnetic  apparatus. — Deter- 
mination of  Joule's  equivalent. — First  law  of  thermo- dynamics. —Illustrations  from 
railway  trains,  cannon-balls,  &c. — Heat  lost  in  -expansion  of  gases. — Joule's  experiment 
on  expansion  without  external  work, — Calculation  of  difference  between  the  two 
specific  heats. — True  specific  heat  of  a  gas. — Thermic  engines. — Definition  of  efficiency. 
—  Carnot's  principles. — Reversibility  a  test  of  maximum  efficiency. — Second  law  of 
thermo -dynamics,  with  appendices. — A  scale  of  temperature  independent  of  the  seleo- 


Vlll  CONTENTS. 

tion  of  any  particular  substance. — Heat  required  for  passing  from  one  given  state  to 
another  not  a  constant  quantity. — Work  done  against  external  pressure  in  expansion. 
— Calculation  of  lowering  of  melting-point  by  pressure. — Calculations  relating  to  liquids 
at  temperatures  below  melting-point. — Animal  heat  and  work. — Chemical  combination. 
— Vegetable  growth. — Coal. — Solar  heat. — Its  sources. — Meteoric  theory. — Contrac- 
tion theory pp.  445-466. 

CHAPTER  XXXIII.     STEAM   AND    OTHER   HEAT  ENGINES. 

Heat-engines  in  general. — Air-engine. — History  of  steam-engine. — Watt's  single-acting 
engine. — Double-acting  engine. — Slide-valve. — Eccentric. — Exhaust-pump. — Governor- 
balls. — Fly-wheel. — Working  expansively. — Compound  engines. — Surface  condensa- 
tion.— Classification  of  steam-engines. — High  and  low  pressure. — Condensing  and  non- 
condensing. — Work  obtained  with  and  without  expansion. — Superheating. — Oscillating 
cylinders. — Example  of  high-pressure  engine. — Rotatory  engine. — Boilers. — Safety- 
valve  and  gauges. — Causes  of  explosions. — Giffard's  injector. — Locomotive,  its  history. 
— Description. — Link-motion  for  reversing. — Gas  engines,  ....  pp.  467-492. 

CHAPTER  XXXIV.     TERRESTRIAL  TEMPERATURES. 

Temperature  of  the  air. — Mean  temperature  of  a  day. — Mean  annual  temperature. — 
Isothermal  lines. — Insular  and  continental  climates. — Underground  temperature. — 
Temperature  upwards  in  the  air.— Cooling  of  air  by  ascent. — Causes  of  winds. — Land 
and  sea  breezes. — Monsoons. — Trade-winds. — Effect  of  earth's  rotation. — General 
circulation  of  air  over  the  earth. — Centrifugal  theory  of  atmospheric  distribution. — 
Indraught  along  earth's  surface  towards  the  poles.' — Origin  of  cyclones. — Anemom- 
eters,   pp.  493-504. 


TABLE  OF  CONSTANTS 


The  pressure  of  one  atmosphere,  or  760  millimetres  (29 '922  inches)  of  mercury,  is  1'033 
kilogramme  per  square  centimetre,  or  1473  Ibs.  per  sq.  inch. 

The  weight  of  a  litre  of  dry  air,  at  this  pressure  (at  Paris)  and  0°  C.,  is  1'293  gramme. 

Dry  air  at  constant  pressure  expands  by  '003665  (or  -— )  of  its  volume  at  0°  C.,  for  each 
degree  Cent. 

The  specific  heat  of  dry  air  at  constant  pressure  is  '2375, 

The  specific  heat  of  dry  air  at  constant  volume  is  '168. 

The  ratio  of  these  numbers  is  T41,  and  their  difference  '0695. 

The  latent  heat  of  fusion  of  ice  is  79°;25  C. 

The  latent  heat  of  steam  at  one  atmosphere  is  637°  C. 


FEENCH  AND  ENGLISH  MEASUKES. 


A.  DECIMETRE  DIVIDED  INTO  CENTIMETRES  AND  MILLIMETRES. 


nTtT^HL-i--2|-      !-!!—-.  ^l   ,.|       1        j'   '1        |       V 

I  I  ,  HI  |   '  I  M  '   I  I  I   M  I  I  I   I   I  •  I  !   !   I   I  I   I  I  I  I   .  I   II   I..I  I   I  I  I  I  I  I  I    I  I  I  l.U   I  I   I  I   I.I.I   I   I   .  I   I   I  I    I      II 


INCHES  AND  TENTHS. 


TABLE  FOR  THE  CONVERSION  OF  FRENCH  INTO  ENGLISH 
MEASURES, 


MEASURES  OP  LENGTH, 

1  Millimetre  =  '03937079  inch,  or  about  ,V  inch. 

1  Centimetre  =  "3937079  inch, 

1  Decimetre  =  3'93707-9  inches. 

1  Metre  =  39  "37079  inches,  or  3 '2809  feet  nearly. 

1  Kilometre  «=  3937079  inches,  or  1093*6  yards  nearly. 

MEASURES  OF  AREA. 

1  sq.  millimetre  =  '00155006  sq.  inch, 

1  sq.  centimetre  =  '155006  sq.  inch. 

1  sq.  decimetre  =  15 '5006  sq.  inches. 

1  eq.  metre  K  1550'06  sq.  inches,  or  107643  sq.  feet. 


X  FRENCH   AND   ENGLISH   MEASURES. 

MEASURES  OF  VOLUME. 

1  cubic  centimetre     =      '0610271  cubic  inch. 
1  cubic  decimetre        =     61*0271  cubic  inches. 

1  cubic  metre  =     61027'!  cubic  inches,  or  35*3166  cubic  feet. 

The  Litre  (used  for  liquids)  is  the  same  as  the  cubic  decimetre,  and  is  equal  to  176172 
imperial  pint,  or  -220215  gallon. 

MEASURES  OP  WEIGHT  (or  MASS). 

1  milligramme  =  '015432349  grain. 

1  centigramme  =  '15432349  grain. 

1  decigramme  =  1*5432349  grain, 

1  gramme  =  15'432349  grains. 

1  kilogramme  =  15432'349  grains,  or  2-20462125  Ibs.  avoir. 

MEASURES  INVOLVING  REFERENCE  TO  TWO  UNITS. 


1  gramme  per  sq,  centimetre  = 

1  kilogramme  per  sq.  metre  = 

1  kilogramme  per  sq.  millimetre  ^ 

I  kilogrananetre  = 


2-048098  Ibs.  per  sq.  foot. 
•2048098    .. 
204809-8    ii 
7-23314  foot-pounds. 


1  force  de  cheval  =  75  kilogrammetres  per  second,  or  542^  foot-pounds  per  second 
nearly,  whereas  1  horse  power  (English)  =550  foot-pounds  per  second 


TABLE  FOR  THE  CONVERSION  OF  ENGLISH  INTO  FRENCH 
MEASURES 


MEASURES  OF  LENGTH. 

1  inch  =25'39954  millimetres, 
1  foot  =  -30479449  metre. 
1  yard  =  -91438347  metre. 
I  mile  =1-60932  kilometre. 

MEASURES  OF  AREJI, 

1  sq.  inch  =  645-1 37  sq.  millimetres, 
1  sq.  foot  =-0923997  sq.  metre. 
I  sq.  yard  =  '8360973  sq.  metre. 
I  sq.  niile  =  2-5-89895  sq.  kilometres. 


SOLID  MEASURES, 

1  cubic  inch  =  16386'6  cubic  millimetres. 
i  cubic  foot  =  -0283153  cubic  metre. 
1  cubic  yard  =  '7645131  cubic  metre. 


MEASURES  OF  CAPACITY. 

1  pint  =  '5676275  litre 
1  gallon  =4-54102  litres. 
1  bushel  =36-32816  litres. 

MEASURES  OF  WEIGHT. 

1  grain        ='064799  gramme. 

1  oz.  avoir.  =28'3496  grammes. 

1  Ib.  avoir.  =  '453593  kilogramme. 

1  ton  =1-01605  tonne  =  1016-05  kilos. 

MEASURES  INVOLVING  REFERENCE  TO 

TWO   UNITS. 

1  Ib.persq. foot  =  4*88261  kilos,  per  sq.  metre. 
1  Ib.persq.  inch=  '0703095  kilos,  per  sq.  cen- 
timetre. 
1  foot-pound     ='138253  kilo^rauoinetre. 


HEAT. 


CHAPTER     XIX,  /I 

THERMOMETRY. 

175.  Heat — Cold. — The  words  heat  and  cold  express  sensations  so 
well  known  as  to  need  no  explanation ;|but  these  sensations  are  £,  A 
modified  by  subjective  causes,  and  do  not  lurnish  an  invariable  cri-  ,/ 
terion   of  objective  realityQ  In  fact,  we  may  often  see  one  person 
suffer  from  heat  while  another  complains  of  cold.    Even  for  the  same 
person  the  sensations  of  heat  and  cold  are  comparative.     A  tempera- 
ture of  50°  Fahr.  suddenly  occurring  amid  the  heat  of  summer  pro- 
duces a  very  decided  sensation  of  cold,  whereas  the  same  temperature 

in  winter  has  exactly  the  opposite  effect.  We  may  mention  an  old 
experiment  upon  this  subject,  which  is  at  once  simple  and  instructive. 
If  we  plunge  one  hand  into  water  at  32°  Fahr.,  and  the  other  into 
water  at  about  100°;  and  if  after  having  left  them  some  time  in  this 
position  we  immerse  them  simultaneously  in  water  at  70°,  they  will 
experience  very  different  sensations.  The  hand  which  was  formerly 
in  the  cold  water  now  experiences  a  sensation  of  heat;  that  which 
was  in  the  hot  water  experiences  a  sensation  of  cold,  though  both  are 
in  the  same  medium.  This  plainly  shows  that  the  sensations  of  heat 
and  cold  are  modified  by  the  condition  of  the  observer,  and  conse- 
quently cannot  serve  as  a  sure  guide  in  the  study  of  calorific  phe- 
nomena. Kecourse  must  therefore  be  had  to  some  more  constant 
standard  of  reference,  and  such  a  standard  is  furnished  by  the  ther- 
mometer. 

176.  Temperature. — If  several  bodies  heated  to  different  degrees  are 
placed  in  presence  of  each  other,  an  interchange  of  heat  takes  place 
between  them,    by  which   they  undergo  modifications  of  opposite 
kinds ;  those  that  are  hottest  grow  cooler,  and  those  that  are  coldest 
grow  warmer;  and  after  a  longer  or  shorter  time  these  inverse  pheno- 
mena cease  to  take  place,  and  the  bodies  come  to  a  state  of  mutual 

16 


242  THERMOMETRT. 

equilibrium.  They  are  then  said  to  be  a,t  the  same  temperature.  If 
a  source  of  heat  is  now  brought  to  act  upon  them,  their  temperature 
is  said  to  rise;  if  they  are  left  to  themselves  in  a  colder  medium,  they 
all  grow  cold,  and  their  temperature  is  said  to  fall.  Two  bodies  are 
said  to  have  the  same  temperature  if  when  they  are  placed  in  contact 
no  heat  passes  from  the  one  to  the  other.  If  when  two  bodies  are 
: placed  i&JbtiEgfeitet,  lieat  passes  from  one  to  the  other,  that  which  gives 
JiQat.to  t,tUe  other -ist  said  to  have  the  higher  temperature.  Heat 
d \vays,  •teiKls,  to'  lf> ass*  from  bodies  of  higher  to  those  of  lower  tem- 
perature. 

177.  Expansion. — At  the  same  time  that  bodies  undergo  these 
changes  in  temperature,  which  may  be  verified  by  the  different 
impressions  which  they  make  upon  our  organs,  they  are  subjected 
to  other  modifications  which  admit  of  direct  measurement,  and  which 
serve  as  a  means  of  estimating  the  changes  of  temperature  themselves. 
These  modifications  are  of  different  kinds,  and  we  shall  have  occasion 
to  speak  of  them  all  in  the  course  of  this  work ;  but  that  which  is 
especially  used  as  the  basis  of  therm ometric  measurement  is  change  of 
,  volume.  In  general,  when  a  body  is  heated,  it  increases  in  volume; 
and,  on  the  other  nand,  when  it  is  cooled  its  volume  diminishes.  The 
expansion  of  bodies  under  the  action  of  heat  may  be  illustrated  by 
the  following  experiments. 

1.  Solid  Bodies. — We  take  a  ring  through  which  a  metal  sphere 


Fig.  182.— Gravesande's  Ring. 


just  passes.  This  latter  is  heated  by  holding  it  over  a  spirit-lamp, 
and  it  is  found  that  after  this  operation  it  will  no  longer  pass  through 
the  ring.  Its  volume  has  increased.  If  it  is  now  cooled  by  immer- 
sion in  water,  it  resumes  its  former  volume,  and  will  again  pass 


EXPANSION   OF   LIQUIDS. 


243 


through  the  ring.  If,  while  the  sphere  was  hot,  we  had  -heated  the 
ring  to  about  the  same  degree,  the  ball  would  still  have  been  able  to 
pass,  their  relative  dimensions  being  unaltered.  This  little  apparatus 
is  called  Gravesande's  Ring. 

2.  Liquids. — A  liquid,  as  water  for  instance,  is  introduced  into  the 


Fig.  183. — Expansion  of  Liquids. 


Fig.  184.— Expansion  of  Gases. 


apparatus  shown  in  Fig.  183,  so  as  to  fill  at  once  the  globe  and  a 
portion  of  the  tube  as  far  as  a.  The  instrument  is  then  immersed  in 
a  vessel  containing  hot  water,  and  at  first  the  extremity  of  the  liquid 
column  descends  for  an  instant  to  6;  but  when  the  experiment  has 
continued  for  some  time,  the  liquid  rises  to  a  point  a'  at  a  con- 
siderable height  above.  This  twofold  phenomenon  is  easily  explained. 
The  globe,  which  receives  the  first  impression  of  heat,  increases  in 
volume  before  any  sensible  change  can  take  place  in  the  temperature 
of  the  liquid.  The  liquid  consequently  is  unable  to  fill  the  entire 


244 


THERMOMETRY. 


\L 


capacity  of  the  globe  and  tube  up  to  the  original  mark,  and  thus 
the  extremity  of  the  liquid  column  is  seen  to  fall.  But  the  liquid 
receiving  in  its  turn  the  impression  of  heat,  expands  also,  and  as  it 
passes  the  original  mark,  we  may  conclude  that  it  not  only  expands, 
but  expands  more  than  the  vessel  which  contains  it. 

§T~Gfases. — Th e  globe  in  Fig.  184  contains  air,  which  is  separated 
from  the  external  air  by  a  small  liquid  index.  We  have  only  to 
warm  the  globe  with  the  hands  and  the  index  will  be  seen  to  be 
pushed  quickly  upwards,  thus  showing  that  gases  are  exceedingly 
expansible. 

178.  General  Idea  of  the  Thermometer. — Since  the  volume  of  a 
body  is  always  changed  by  heat,  it  follows  that  when  a  body  is  sub- 
jected to  variations  of  temperature,  it  undergoes  at  the  same  time 
corresponding  variations  of  volume.  If  we  suppose  that  the  different 
volumes  successively  assumed  by  the  body  can  easily  be  measured, 
we  may  indicate  the  temperature  by  stating  the 
volume.  And  the  body  will  not  only  indicate  its 
own  temperature  by  this  means,  it  will  also  exhibit 
the  temperature  of  the  bodies  by  which  it  is  sur- 
rounded, and  which  are  in  equilibrium  with  it  as 
regards  temperature;  that  is,  which  do  not  experi- 
ence those  inverse  changes  mentioned  in  §  1 76.  Such 
is  the  most  general  idea  of  the  thermometer,  which 
may  be  defined  as  a  body  which,  under  the  action 
of  heat,  exhibits  changes  of  volume  which  can  be 
ascertained  and  measured. 

179.  Choice  of  the  Thermometric  Substance. — Any 
substance  whatever  will  serve  as  a  thermometric 
substance,  and  in  fact  there  are  several  kinds  of 
thermometers,  founded  upon  the  expansion  of  dif- 
ferent substances.  In  order,  however,  that  thermo- 
metric indications  may  be  comparable  with  each 
other,  it  is  necessary  to  adopt  a  standard  substance 
or  combination  of  substances,  and  physicists  have  by 
common  consent  adopted  as  the  standard  of  reference 
the  apparent  expansion  of  mercury  contained  in  a  glass  vessel.  The 
instrument  which  exhibits  this  expansion  is  called  the  mercurial 
thermometer.  It  consists  essentially,  as  shown  in  Fig.  185,  of  a  tube 
of  very  small  diameter,  terminating  in  a  bulb  or  reservoir  of  a  cylin- 
drical, spherical,  or  any  other  form.  The  reservoir  and  a  portion  of 


Fig.  185.— Memirial 
Thermometers. 


CONSTRUCTION   OF  THE  THERMOMETER.  245 

the  tube  are  filled  with  mercury.  If  the  temperature  varies,  the 
level  of  the  liquid  will  rise  or  fall  in  the  tube,  and  the  points  at 
which  it  remains  stationary  can  be  easily  identified  by  means  of  a 
scale  attached  to  or  engraved  on  the  tube. 

The  choice  of  mercury  as  a  thermometric  substance  is  extremely 
suitable.     It  is  a  liquid  which  may  easily  be  procured  in  a  state  of 
purity.     It  is  a  very  good  conductor  of  heat,  and  consequently  soon    &*ju 
comes  into  equilibrium   of  temperature  with  the  bodies  which  it   • 
touches.     Besides,  its  calorific  capacity  is  very  small,  so  that  if  it  be  /  ' 
brought  into   contact  with  a  heated  body,  for  instance,  at  whose 
expense  it  grows  hot,  this  body  experiences  in  consequence  only  a 
very  slight  change  of  temperature,  which  may  generally  be  neglected. 
A     180.  Construction  of  the  Mercurial  Thermometer. — The  construction 
of  a  mercurial  thermometer  is  an  operation  of  great  delicacy,  and 
comprises  several  different   processes,  which  we   shall   successively 
indicate. 

1.  Choice  of  the  Tube. — The  first  object  is  to  procure  a  tube  of  as 
uniform  bore  as  possible.     In  order  to  ascertain  whether  this  con- 
dition is  fulfilled,  a  small  column  of  mercury  is  introduced  into  the 
tube,  and  its  length  in  different  parts  of  the  tube  is  measured.     If 
these  lengths  are  exactly  equal,  the  tube  must  be  of  uniform  bore. 
This  is  not  generally  the  case,  and  we  have  to  content  ourselves  with 
an  approximation  to  this  result;  but  we  must  reject  tubes  in  which 
the  differences  of  length  observed  are  too  great.     When  a  suitable 
tube  has  been  obtained,  a  reservoir  is  either  blown  at  one  end  or 
attached  by  melting,  the  former  plan  being  usually  preferable. 

When  a  thermometer  of  great  precision  is  required,  the  tube  is 
first  calibrated;  that  is,  divided  into  parts  of  equal  volume. 

2.  Introduction  of  the  Mercury. — At  the  upper  extremity  of  the 
tube  a  bulb  has  been  blown,  drawn  out  to  a  point,  at  which  there  is 
a  small  opening;  this  bulb  is  gently  heated,  arid  the  point  is  then 
immersed  in  a  vessel  containing  mercury  (Fig.  186).     The  air  in  the 
tube  growing  cold,  suffers  a  diminution  at  once  of  volume  and  of 
pressure,  so  that  mercury  is  forced  into  the  bulb  by  the  atmospheric 
pressure.     The  end  of  the  point  is  then  closed  to  prevent  the  escape 
of  mercurial  vapours,  and  the  reservoir  and  tube,  still  remaining 
empty,  are  heated  in  a  gas  or  charcoal  furnace  (Fig.  187),  so  as  to 
rarefy  the  contained  air.     The  liquid  in  the  bulb  is  then  heated,  and 
on  setting  the  instrument  upright,  and  allowing  it  to  cool,  a  portion 
of  the  mercury  enters  the  reservoir  in  consequence  of  the  contraction 


246 


THERMOMETRY. 


of  the  air.  The  liquid  in  the  reservoir  is  then  heated  to  ebullition, 
the  air-  is  expelled  from  the  reservoir  and  tube  by  the  vapour  of 
mercury,  and  on  placing  th^  instrument  in  an  upright  position,  the 


Fig.  186.— Introduction  of  the  Mercury. 


mercury  during  the  process  of  cooling  enters  the  reservoir  and  com- 
pletely fills  it,  If  a  bubble  of  air  still  remains,  as  is  often  the  case, 
it  may  be  expelled  by  repeating  the  same  operation  several  times. 
The  quantity  of  mercury  to  be  left  is  then  regulated  according  to  the 


V 


Fig.  187. — Furnace  for  heating  Thermometers. 

temperatures  which  the  instrument  is  intended  to  indicate;  the  bulb 
at  the  upper  end  is  removed,  and  the  tube,  having  been  drawn  out  to 
a  point,  is  hermetically  sealed  at  the  moment  when  the  mercury 
reaches  its  extremity,  so  as  to  leave  no  air  in  the  interior. 


CONSTRUCTION   OF  THE  THERMOMETER. 


247 


^  3.  Determination  of  the  Fixed  Points. — The  instrument,  under 
these  conditions,  and  with  any  scale  of  equal  parts  marked  on  the 
tube,  would  of  course  indicate  variations  of  temperature,  but  these 
indications  would  be  arbitrary,  and  two  thermometers  so  constructed 
would  in  general  give  different  indications. 

In  order  to  insure  that  the  indications  of  different  thermometers 
shall  be  comparable,  it  has  been  agreed  to  adopt  two  standard  tem- 
peratures, which  can  easily  be  reproduced  and  maintained  for  a  con- 
siderable time,  and  to  denote  them  by  fixed  numbers.  These  two 
temperatures  are  the  freezing-point  and  boiling-point  of  water ;  or  to 
speak  more^  strictly,  the  temperature  of  melting  ice,  and  the  tem- 
perature of  the  steam  given  off  by 
water  boiling  under  average  atmos- 
pheric pressure.  It  has  been  observed 
that  if  the  thermometer  be  surrounded 
with  melting  ice  (or  melting  snow), 
the  mercury,  under  whatever  circum- 
stances the  experiment  is  performed, 
invariably  stops  at  the  same  point, 
and  remains  stationary  there  as  long  as 
the  melting  continues.  This  then  is  a 
fixed  temperature.  On  the  Centigrade 
scale  it  is  called  zero,  on  Fahrenheit's 
scale  32°. 

In  order  to  mark  this  point  on  a 
thermometer,  it  is  surrounded  by  melt- 
ing ice,  which  is  contained  in  a  perforated  vessel,  so  as  to  allow 
the  water  produced  by  melting  to  escape.  When  the  level  of  the 
mercury  ceases  to  vary,  a  mark  is  made  on  the  tube  with  a  fine 
diamond  at  the  extremity  of  the  mercurial  column.  This  is  frequently 
called  for  brevity  the  freezing-point. 

It  has  also  been  observed  that  if  water  be  made  to  boil  in  an  open 
metallic  vessel,  under  average  atmospheric  pressure  (760  millimetres, 
or  29'922  inches),  and  if  the  thermometer  be  plunged  into  the  steam, 
the  mercury  stands  at  the  same  point  during  the  entire  time  of 
ebullition,  provided  that  the  external  pressure  does  not  change.  This 
second  fixed  temperature  is  called  1 00°  in  the  Centigrade  scale  (whence 
the  name),  and  212°  on  Fahrenheit's  scale.  In  order  to  mark  this 
second  point  on  the  thermometer,  an  apparatus  is  employed  which 
was  devised  by  Gay-Lussac,  and  perfected  by  Regnault.  It  consists 


Fig.  188. — Determination  of  Freezing- 
point. 


248 


THERMOMETRY. 


of  a  copper  boiler  (Fig.  189)  containing  water  which  is  raised  to 
ebullition  by  means  of  a  furnace.  The  steam  circulates  through  a 
double  casing,  and  escapes  by  a  tube  near  the  bottom.  The  ther- 
mometer is  fixed  in  the  interior  casing,  and  when  the  mercury  has 


Fig.  189. — Determination  of  Boiling-point 

become  stationary,  a  mark  is  made  at  the  point  at  which  it  stops, 
which  denotes  what  is  commonly  called  for  brevity  the  boiling-point. 
It  now  only  remains  to  divide  the  portion  of  the  instrument  between 
the  freezing  and  boiling  points  into  equal  parts  corresponding  to 
single  degrees,  and  to  continue  the  division  beyond  the  fixed  points. 
Below  the  zero  point  are  marked  the  numbers  1,2,  3,  &c.  These 


tMJLtsw^A 


CONSTRUCTION   OF   THE  THERMOMETER.  249 

temperatures  are  generally  expressed  with  the  sign  — .  Thus  the 
temperature  of  17°  below  zero  is  written  — 17°. 

A  small  manometric  tube,  open  at  both  ends,  serves  to  show,  by 
the  equality  of  level  of  the  mercury  in  its  two  branches,  that  the 
ebullition  is  taking  place  at  a  pressure  equal  to  that  which  prevails 
externally,  and  consequently  that  the  steam  is  escaping  with  suffi- 
cient freedom.  It  frequently  happens  that  the  external  pressure  is 
not  exactly  760  millimetres,  in  which  case  the  boiling-point  should  be 
placed  a  little  above  or  a  little  below  the  point  at  which  the  mer- 
cury remains  stationary,  according  as  the  pressure  is  less  or  greater 
than  this  standard  -pressure.  When  the  difference  on  either  side  is 
inconsiderable,  the  position  of  the  boiling-point  is  calculated  by  the 
rule,  that  a  difference  of  20'6  millimetres,  either  above  or  below  the 
normal  pressure,  causes  a  difference  of  1°  in  the  temperature  of  the 
steam  produced.  We  shall  return  to  this  point  in  Chap.  xxvi. 

181.  Adjustment  of  the  Quantity  of  Mercury. — In  order  to  avoid 
complicating  the  above  explanation,  we  have  omitted  to  consider  an 
operation  of  great  importance,  which  should  precede  those  which  we 
have  just  described.  This  is  the  determination  of  the  volume  which 
must  be  given  to  the  reservoir,  in  order  that  the  instrument  may  have 
the  required  range.  WHien  the  reservoir  is  cylindrical,  this  is  very  easily 
effected  in  the  following  manner.  Suppose  we  wish  the  thermometer 
to  indicate  temperatures  comprised  between  — 20°  and  130°  Cent.,  so 
that  the  range  is  to  be  150°;  the  reservoir  is  left  open  at  O  (Fig.  190), 


and  is  filled  through  this  opening,  which  is  then  hermetically  sealed. 
The  instrument  is  then  immersed  in  two  baths  whose  temperatures 
differ  by  50°,  for  instance,  and  the  mercury  rises  through  a  distance 
mm'.  This  length,  if  the  quantity  of  mercury  in  the  reservoir  be 
exactly  sufficient,  should  be  the  third  part  of  the  length  of  the  stem. 
But  the  quantity  of  mercury  in  the  reservoir  is  always  taken  too  large 
at  first,  so  that  it  has  only  to  be  reduced,  and  thus  the  space  traversed 
by  the  liquid  is  at  first  too  great.  Suppose  it  to  be  equal  to  fths  of 
the  length  of  the  stem.  The  degrees  will  then  be  too  long,  in  the 
ratio  f  :  J=-f-.  That  is,  the  reservoir  is  -f-  of  what  it  should  be.  We 
therefore  measure  off  £ths  of  the  length  of  the  reservoir,  beginning 
at  the  end  next  the  stem ;  this  distance  is  marked  by  a  line,  and  the 
end  O  is  then  broken  and  the  mercury  suffered  to  escape.  The  glass 


250 


THERMOMKTRY. 


ZO! 


Z1Z:. 


is  then  melted  down  to  the  marked  line,  and  the  reservoir  is  thus 
brought  to  the  proper  dimensions.  It  only  remains  to  regulate  the 
quantity  of  mercury  admitted,  by  making  it  fill  the  tube  at  the 
highest  temperature  which  the  instrument  is  intended  to  indicate. 

If  the  reservoir  were  spherical,   which   is  a  shape  generally  ill 
adapted  for  delicate  thermometers,  the  foregoing  process  would  be 
inapplicable,  and  it  would  be  necessary  to  deter- 
mine the  proper  size  by  trial. 

x/  182.  Thermometric    Scales.  —  In   the   Centigrade 

scale  the  freezing-point  is  marked  0°,  and  the  boil- 
ing-point 100°.  In  Reaumur'' s  •  scale,  which  is  still 
sometimes  used  abroad,  the  freezing-point  is  also 
marked  0°,  but  the  boiling-point  is  marked  80°. 
Hence,  5  degrees  on  the  former  scale  are  equal  to 
4  on  the  latter,  and  the  reduction  of  temperatures 
from  one  of  these  scales  to  the  other  can  be  effected 
by  multiplying  by  -J  or  f. 

For  example,  the  temperature  7o°  Centigrade  is 
the  same  as  60°  Reaumur,  since  75  X  f  =  60;  and  the 
temperature  36°  Reaumur  is  the  same  as  45°  Centi- 
grade, since  3G  X  |  =  45. 

The  relation  between  either  of  these  scales  and 
that  of  Fahrenheit  is  rather  more  complicated,  inas- 
much as  Fahrenheit's  zero  is  not  at  freezing-point, 
but  at  32  of  his  degrees  below  it. 

As  regards  intervals  of  temperature,  1 80  degrees 
Fahrenheit  are  equal  to  100  Centigrade,  or  to  80 
Reaumur,  and  hence,  in  lower  terms,  9  degrees 
Fahrenheit  are  equal  to  5  Centigrade,  or  to  4 
Re'aumur. 

The  conversion  of  temperatures  themselves  (as 
distinguished  from  intervals  of  temperature)  will  be 
best  explained  by  a  few  examples. 

Example  1.     To  find  what  temperatures  on  the 
other  two  scales  are  equivalent  to  the  temperature  50°  Fahrenheit. 

Subtracting  32,  we  see  that  this  temperature  is  18  Fahrenheit 
degrees  above  freezing-point,  and  as  this  interval  is  equivalent  to 
]  8  X  £ ,  that  is  10  Centigrade  degrees,  or  to  18  X  i,  that  is  8  Re'aumur 
degrees,  the  equivalent  temperatures  are  respectively  10°  Centigrade 
and  8°  Reaumur. 


Fig.  191. 
Thermometric  Scales. 


THE   THERMOMETRIC   SCALES.  251 

Example  2.  To  find  the  degree  on  Fahrenheit's  scale,  which  is 
equivalent  to  the  temperature  25°  Centigrade. 

An  interval  of  25  Centigrade  degrees  is  equal  to  25  X  -§-,  that  is 
45  Fahrenheit  degrees,  and  the  temperature  in  question  is  above 
freezing-point  by  this  amount.  The  number  denoting  it  on  Fahren- 
heit's scale  is  therefore  32  +  45,  that  is  77°. 

The  rules  for  the  conversion  of  the  three  thermometric  scales  may 
be  summed  up  in  the  following  formulae,  in  which  F,  C,  and  R-  denote 
equivalent  temperatures  expressed  in  degrees  of  the  three  scales:  — 


C=|R  =  f-  (F-32). 
R  =  £C=£(F-32). 

It  is  usual  in  stating  temperatures  to  indicate  the  scale  referred  to 
by  the  abbreviations  Fahr.,  Cent,  Reau.,  or  more  briefly  by  the 
initial  letters  F.,  C.,  R 

X     183.  Apparent  Expansion  of  Mercury.   Degree  of  the  Mercurial  Ther- 
mometer. —  The  indications  of  the  mercurial  thermometer  depend  not 
upon  the  real  but  upon  the  apparent  expansion  of  mer- 
cury, that  is,  upon  the  difference  between  the  expansion 
of  the  mercury  and  that  of  the  glass  in  which  it  is  con-    1i 
tained. 

To  understand  the  physical  meaning  of  a  degree,  sup- 
pose that  we  have  a  thermometric  tube  (Fig.  192)  divided 
into  parts  of  equal  capacity,  and  that  by  gauging  the 
reservoir  we  have  ascertained  its  capacity  to  be  equal  to 
N  of  these  parts.  Mercury  is  introduced,  and  when  the 
instrument  is  surrounded  with  melting  ice  the  mercury 
fills  the  bulb  and  n  parts  of  the  tube.  The  instrument  is 
then  raised  to  the  temperature  of  100°  C.,  and  the  mercury 
expands  so  as  to  occupy  n'  parts  of  the  stem.  The  appar- 
ent volumes  of  the  mercury  at  0°  and  100°  Centigrade  are 
therefore  K  +  n  and  N  +  u'  respectively,  and  the  apparent 
increase  of  volume  is  ri  —  n.  The  apparent  increase  per 

unit  volume  is  therefore  ^      ,  and  as  this  is  the  increase  for  100°  the 
apparent  expansion  per  degree  Centigrade  is  1{^       rn-     This  quantity 


is  found  by  experiment  to  be  about  equal  to  g^.     Each  degree 
Centigrade  represents  then  a  difference  of  apparent  volume  of  the 

mercury  equal  to  about  g^  of  its  volume  at  freezing-point. 


252  THERMOMETRT. 

184.  Comparability  of  Mercurial  Thermometers. — This  enables  us  to 
examine  the  important  question,  whether  different  thermometers  are 
comparable  with  each  other,  that  is,  whether  they  will  indicate  the 
same  temperature  under  the  same  conditions.     This  must  evidently 
be  the  case  where  the  glass  employed  for  the  construction  of  the  tubes 
is  absolutely  the  same.     The  agreement  will  likewise  be  exact,  even 
when  the  apparent  expansions  due  to  the  quality  of  the  glass  em- 
ployed in  each  case  are  not  the  same,  provided  that  they  preserve  a 
constant  ratio  at  different  temperatures. 

Experiment  alone  can  teach  us  whether  this  disagreement  actually 
exists,  and  in  what  degree.  The  result  of  Regnault's  investigations 
upon  this  point  tends  to  show  that  up  to  300°  Cent,  this  disagree- 
ment is  almost  nothing,  or,  at  any  rate,  may  be  neglected  with  perfect 
safety;  above  this  point  a  slight  difference  is  observed,  which  increases 
to  about  3°  or  4°  at  the  temperature  of  350°,  that  is,  at  the  superior 
limit  to  the  use  of  the  mercurial  thermometer. 

This  defect  in  the  comparability  of  thermometers,  slight  as  it  is, 
must  be  attributed  to  irregularities  in  the  expansion  of  the  glass. 
The  influence  of  these  irregularities  would  obviously  be  less  sensible 
with  a  more  expansible  material  than  mercury,  and  this  is  the  reason 
that  in  experiments  where  great  precision  is  necessary  air-thermo- 
meters are  employed,  which  at  the  same  time  serve  to  indicate  the 
highest  temperatures,  whereas  mercury  cannot  be  employed  beyond 
350°,  its  boiling-point. 

185.  Displacement  of  the  Zero  Point. — A  thermometer  left  to  itself 
after  being  made,  gradually  undergoes  a  contraction  of  its  capacity, 
leading  to  a  uniform  error  of  excess  in  its  indications.     This  pheno- 
menon is  attributable  to  molecular  change  in  the  glass,  which  has,  so 
to  speak,  been  tempered  in  the  construction  of  the  instrument,  and 
to  atmospheric  pressure  on  the  exterior  of  the  bulb,  which  is  unre- 
sisted  by  the  internal  vacuum.     The  progress  of  this  change  ceases  at 
the  end  of  a  certain  time,  about  fifteen  or  eighteen  months,  and  the 
displacement  is  always  inconsiderable,  never  amounting  to  a  degree. 
In  precise  experiments,  however,  it  is  necessary  to  verify  the  position 
of  the  zero  point  in  the  thermometer  employed,  and,  in  the  observa- 
tion of  temperatures,  to  take  into  consideration  the  slight  displace- 
ment which  may  have  occurred. 

X  186.  Sensibility  of  the  Thermometer. — The  power  of  the  instrument 
to  detect  very  small  differences  of  temperature  may  be  regarded  as 
measured  by  the  length  of  the  degrees,  which  is  proportional  to  the 


v  tz  n  o  J  »  i    w-J  r   v/  «  u  t  r  w  n  i  M  i  f+ 

DEPARTMENT  OF  PHVSiCi* 
WEIGHT  THERMOMETER.  253 

capacity  of  the  bulb  directly  and  to  the  section  of  the  tube  inversely. 
In  fact,  if  I  denote  the  length  of  one  degree,  and  s  the  sectional  area 

of  the  tube,  I  s  will  be  the  volume  of  one  degree,  which  is  g4g()  C, 
where  C  denotes  the  capacity  of  the  bulb,  together  with  as  much  of 
the  tube  as  is  below  the  freezing-point.  Hence,  Z  =  64867>  which 
varies  directly  as  C,  and  inversely  as  s. 

Quickness  of  action,  on  the  other  hand,  requires  that  the  bulb  be 
small  in  at  least  one  of  its  dimensions,  so  that  no  part  of  the  mercury 
shall  be  far  removed  from  the  exterior,  and  also  that  the  glass  of  the 
bulb  be  thin. 

Quickness  of  action  is  important  in  measuring  temperatures  which 
vary  rapidly.    It  should  also  be  observed  that,  as  the  thermometer,  in 
coming  to  the  temperature  of  any  body,  necessarily  causes 
an  inverse  change  in  the  temperature  of  that  body,  it  fol- 
lows  that  when  the  mass  of  the  body  to  be  investigated  is 
very  small,  the  thermometer  itself  should  be  of  extremely 
small  dimensions,  in  order  that  it  may  not  cause  a  sensible 
variation  in  the  temperature  to  be  ascertained. 
)C  187.  Weight  Thermometer. — In  this  thermometer,  which 
often  takes  the  place  of  the  ordinary  thermometer  in  physi- 
cal investigations,  the  stem  is  done  away  with,  and  the 
mercury  contained  in  the  reservoir  overflows  into  a  small     Fig- 193- 
cup,  where  it  is  collected ;   and  the  temperature  is  deduced    mometer. 
from  the  weight  of  the  mercury  which  thus  escapes.     Let 
P  be  the  weight  of  the  mercury  which  fills  the  reservoir  at  freezing- 
point,  and  TT  the  weight  which  issues  when  the  instrument  is  placed 
in  the  steamer  in  order  to  determine  the  boiling-point.    The  apparent 
expansion  between  these  points   is   evidently  represented   by  the 

fraction  -p^.,  and,  consequently,  the  value  of  a  degree  Centigrade  is 
the  one-hundredth  part  of  this  fraction,  that  is  jooTpT^-)-  Suppose 
now  that  the  instrument,  containing  again  a  weight  P  of  mercury  at 
zero  is  placed  in  a  bath  whose  temperature  we  wish  to  determine,  and 
that  a  weight  p  of  mercury  flows  over.  The  whole  apparent  expan- 
sion is  p-j-,  and  dividing  this  by  the  value  of  a  degree,  we  obtain 
the  temperature  required,  which  is  thus  expressed  by  the  formula 


254 


THERMOMETRY. 


K 


188.  Alcohol  Thermometer. — In  the  construction  of  thermometers 
other  liquids  may  be  introduced  instead  of  mercury,  and  alcohol  is 
very  frequently  employed  for  this  purpose.  But  if  an  alcohol  ther- 
mometer were  constructed  so  as  to  agree  with  a  mercurial  thermometer 
at  two  fixed  temperatures,  and  were  graduated  by  dividing  the  inter- 
vening space  into  equal  parts,  and  continuing  the  equal  graduations 
both  ways,  it  would  be  found  to  give  different  readings  from  a  mer- 
curial thermometer,  except  at  or  very  near  the  two  fixed  temperatures. 
This  fact  may  be  expressed  by  saying,  that  alcohol  does  not  expand 
equally  for  equal  increments  of  temperature  as  indicated  by  a  mer- 
curial thermometer ;  or,  more  symmetrically,  by  saying  that  intervals 
of  temperature  which  are  equal  as  measured  by  the  expansion  of 
mercury,  are  not  equal  as  measured  by  the  expansion  of  alcohol. 
In  practice,  alcohol  thermometers  are  graduated  by  comparison 
with  mercurial  thermometers,  and  the  de- 
grees of  an  alcohol  thermometer  have  conse- 
quently unequal  volumes  in  different  parts 
of  the  scale.  The  degrees,  in  fact,  increase  in 
length  as  we  ascend  on  the  scale. 

Alcohol  has  the  disadvantage  of  being 
slower  in  its  action  than  mercury,  on  ac- 
count of  its  inferior  conductivity;  but  it  can 
be  employed  for  lower  temperatures  than 
mercury,  as  the  latter  congeals  at  —  39°  Cent. 
(—38°  Fahr.),  whereas  the  former  has  never 
congealed  at  any  temperature  yet  attained. 

189.  Self-registering  Thermometers.  —  It  is 
often  important  for  meteorological  purposes 
to  have  the  means  of  knowing  the  highest  or 

o  O 

the  lowest  temperature  that  occurs  during  a 
given  interval.  Instruments  intended  for 
this  purpose  are  called  maximum  and  mini- 
mum thermometers. 

The  oldest  instrument  of  this  class  is  Six's 
(Fig.  19-tA),  which  is  at  once  a  maximum 
and  a  minimum  thermometer.  It  has  a  large 
cylindrical  bulb  C  filled  with  alcohol,  which 
also  occupies  a  portion  of  the  tube.  The 

remainder  of  the  tube  is  partly  filled  with  mercury,  which  occupies 
a   portion  of   the  tube  shaped   like   the   letter    U,  one  extremity 


Fig.  194A.— Six's  Self-registering 
Thermometer. 


SELF-REGISTERING  THERMOMETERS,  255 

of  the  mercurial  column  being  in  contact  with  the  alcohol  already 
mentioned,  while  the  other  extremity  is  in  contact  with  a  second 
column  of  alcohol;  and  beyond  this  there  is  a  small  space  occupied 
only  with  air,  so  as  to  leave  room  for  the  expansion  of  the  liquids. 
When  the  alcohol  in  the  bulb  expands  it  pushes  the  mercurial  column 
before  it,  and  when  it  contracts  the  mercurial  column  follows  it.  The 
extreme  points  reached  by  the  two  ends  of  the  mercurial  column  are 
registered  by  a  pair  of  light  steel  indices  c,  d  (shown  on  an  enlarged 
scale  at  K),  which  are  pushed  before  the  ends  of  the  column,  and  then 
are  held  in  their  places  by  springs,  which  are  just  strong  enough  to 
prevent  slipping,  so  that  the  indices  do  not  follow  the  mercury  in  its 
retreat.  One  of  the  indices  d  registers  the  maximum  and  the  other 
c  the  minimum  temperature  which  has  occurred  since  the  instrument 
was  last  set.  The  setting  consists  in  bringing  the  indices  into  contact 
with  the  ends  of  the  mercurial  column,  and  is  usually  effected  by 
means  of  a  magnet.  This  instrument  is  now,  on  account  of  its  com- 
plexity, little  used.  It  possesses,  however,  the  advantages  of  being 
equally  quick  (or  slow)  in  its  action  for  maximum  and  minimum 
temperatures,  which  is  an  important  property  when  these  tempera- 
tures are  made  the  foundation  for  the  computation  of  the  mean  tem- 
perature of  the  interval,  and  of  being  better  able  than  most  of  the 
self-registering  thermometers  to  bear  slight  jolts  without  disturbance 
of  the  indices. 

><     Rutherford's  self- registering  thermometers  are  frequently  mounted 
together  on  one  frame,  as  in  Fig.  195,  but  are  nevertheless  distinct 


(7) 


c 

Fig.  195.— Rutherford's  Maximum  and  Minimum  Thermometers. 

instruments.  His  minimum  thermometer,  which  is  the  only  mini- 
mum thermometer  in  general  use,  has  alcohol  for  its  fluid,  and  is 
always  placed  with  its  tube  horizontal,  or  nearly  so.  In  the  fluid 
column  there  is  a  small  index  n  of  glass  or  enamel,  shaped  like  a 
dumb-bell. 

When  contraction  occurs,  the  index,  being  wetted  by  the  liquid,  is 
forced  backwards  by  the  contractile  force  of  the  superficial  film  which 
forms  the  extremity  of  the  liquid  column  (§  97) ;  but  when  expansion 


256  THERMOMETR  Y. 

takes  place  the  index  remains  stationary  in  the  interior  of  the  liquid. 
Hence  the  minimum  temperature  is  indicated  by  the  position  of  the 
forward  end  of  the  index.  The  instrument  is  set  by  inclining  it  so 
as  to  let  the  index  slide  down  to  the  end  of  the  liquid  column. 

The  only  way  in  which  this  instrument  is  liable  to  derangement, 
is  by  a  portion  of  the  spirit  evaporating  from  the  column  and  becoming 
condensed  in  the  end  of  the  tube,  which  usually  terminates  in  a 
small  bulb.  When  the  portion  thus  detached  is  large,  or  when  the 
column  of  spirit  becomes  broken  into  detached  portions  by  rough 
usage  in  travelling,  "  let  the  thermometer  be  taken  in  the  hand  by 
the  end  farthest  from  the  bulb,  raised  above  the  head,  and  then 
forcibly  swung  down  towards  the  feet;  the  object  being,  on  the  prin- 
ciple of  centrifugal  force,  to  send  down  the  detached  portion  of  spirit 
till  it  unites  with  the  column.  A  few  throws  or  swinging  strokes 
will  generally  be  sufficient;  after  which  the  thermometer  should  be 
placed  in  a  slanting  position,  to  allow  the  rest  of  the  spirit  still 
adhering  to  the  sides  of  the  tube  to  drain  down  to  the  column.  But 
another  method  must  be  adopted  if  the  portion  of  spirit  in  the  top  of 
the  tube  be  small.  Heat  should  then  be  applied  slowly  and  cautiously 
to  the  end  of  the  tube  where  the  detached  portion  of  spirit  is  lodged; 
this  being  turned  into  vapour  by  the  heat  will  condense  on  the  sur- 
face of  the  unbroken  column  of  spirit.  Care  should  be  taken  that 
the  heat  is  not  too  quickly  applied.  .  .  .  The  best  and  safest  way  to 
apply  the  requisite  amount  of  heat,  is  to  bring  the  end  of  the  tube 
slowly  down  towards  a  minute  flame  from  a  gas-burner;  or  if  gas  is 
not  to  be  had,  a  piece  of  heated  metal  will  serve  instead/'1 

Rutherford's  maximum  thermometer  is  a  mercurial  thermometer, 
with  the  stem  placed  horizontally,  and  with  a  steel  index  c  in  the 
tube  outside  the  mercurial  column.  When  expansion  occurs,  the 
index,  not  being  wetted  by  the  liquid,  is  forced  forwards  by  the  con- 
tractile force  of  the  superficial  film  which  forms  the  extremity  of  the 
liquid  column  (§97);  but  when  contraction  takes  place,  the  index 
remains  stationary  outside  the  liquid.  Hence  the  maximum  tem- 
perature is  indicated  by  the  position  of  the  backward  end  of  the 
index.  The  instrument  is  set  by  bringing  the  index  into  contact 
with  the  end  of  the  liquid  column,  an  operation  which  is  usually 
effected  by  means  of  a  magnet. 

This  thermometer  is  liable  to  get  out  of  order  after  a  few  years'  use, 
by  chemical  action  upon  the  surface  of  the  index,  which  causes  it  to 

1  Buchan's  Handy  Boole  of  Meteorology,  p.  62. 


SELF-REGISTERING  THERMOMETERa  257 

become  wetted  by  the  mercury,  and  thus  renders  the  instrument 
useless. 

0  Phillips  maximum  thermometer  (invented  by  Professor  Phillips, 
the  eminent  geologist,  and  made  by  Casella)  is  recommended  for  use 
in  the  official  Instructions  for  Talcing  Meteorological  Observations, 
drawn  up  by  Sir  Henry  James  for  the  use  of  the  Royal  Engineers. 
It  is  a  mercurial  thermometer  not  deprived  of  air.  It  has  an  exceed- 


I  «  I  to  I  n  \io\li\  u\  10  I  n  \so  \,oo  \S,o\w\i!»  \fn\ 


Fig.  194  B.—  Phillips'  Maximum  Thermometer. 

ingly  fine  bore,  and  the  mercurial  column  is  broken  by  the  insertion 
of  a  small  portion  of  air.  The  instrument  is  set  by  reducing  this 
portion  of  air  to  the  smallest  dimensions  which  it  can  be  made  to 
assume,  and  is  placed  in  a  horizontal  position.  When  the  mercury 
expands  it  pushes  forwards  this  intervening  air  and  the  detached 
column  of  mercury  beyond  it;  but  when  contraction  takes  place  the 
intervening  air  expands,  and  the  detached  column  remains  unmoved. 

"The  thread  of  mercury  in  these  thermometers  is  easily  broken  at 
any  point  required,  by  simply  raising  the  bulb  end,  and  allowing  the 
mercury  to  run  into  the  open  cell  at  the  end  ;  and,  as  it  descends, 
detaching,  with  a  slight  jerk,  as  much  of  it  as  may  be  thought  neces- 
sary, which  should  be  an  inch,  or  an  inch  and  a  half."1 

The  detached  column  is  not  easily  shaken  out  of  its  place,  and 
when  the  bore  of  the  tube  is  made  sufficiently  narrow  the  instrument 
may  even  be  used  in  a  vertical  position,  a  property  which  is  often  of 
great  service. 

In  Negretti  and  Zambra's  maximum  thermometer  (Fig.  194),  which 
is  employed  at  the  Royal  Observatory,  Greenwich,  there  is  an 


Fig.  194.— Negretti's  Maximum  Thermometer. 

obstruction   in  the  bent   part  of  the  tube,    near  the  bulb,  which 
barely  leaves  room  for  the  mercury  to  pass  when  forced  up  by 

1  Instructions  for  Taking  Meteorological  Observations.  By  Colonel  Sir  Henry  James,  R.E., 
Director  of  the  Ordnance  Survey. 

17 


258  THERMOMETRY. 

expansion,  and  is  sufficient  to  prevent  it  from  returning  when  the 
bulb  cools. 

The  objection  chiefly  urged  against  this  thermometer  is  the  extreme 
mobility  of  the  detached  column,  which  renders  it  very  liable  to 
accidental  displacement;  but  in  the  hands  of  a  skilful  observer 
this  is  of  no  moment.  Dr.  Balfour  Stewart  (Elementary  Treatise 
on  Heat,  p.  20,  21),  says: — "When  used,  the  stern  of  this  instru- 
ment ought  to  be  inclined  downwards.  ...  It  does  not  matter 
if  the  column  past  the  obstruction  go  down  to  the  bottom  of  the  tube; 
for  when-  the  instrument  is  read,  it  is  gently  tilted  up  until  this 
detached  column  flows  back  to  the  obstruction,  where  it  is  arrested, 
and  the  end  of  the  column  will  then  denote  the  maximum  tem- 
perature. In  resetting  the  instrument,  it  is  necessary  to  shake  the 
detached  column  past  the  obstruction  in  order  to  fill  up  the  vacancy 
left  by  the  contraction  of  the  fluid  after  the  maximum  had 
been  reached." 

MERCURIAL  MINIMUM  THERMOMETERS.  —  As  it  is  obvi- 
ously undesirable  that  the  minimum  thermometer  employed 
should  be  slower  in  its  action  than  the  maximum  thermo- 
meter used  in  conjunction  with  it,  several  attempts  have 
been  made  to  construct  a  minimum  thermometer  in  which 
mercury  instead  of  alcohol  shall  be  the  expanding  fluid  (see 
a  description  of  Casella's  mercurial  minimum  thermometer, 
Stewart  on  Heat,  p.  22) ;  but  no  one  has  yet  succeeded  in 
producing  such  an  instrument  fit  for  general  use. 

DEEP-SEA.  AND  WELL  THERMOMETERS. — The  instruments 
which  have  been  most  successfully  employed  for  the  obser- 
vation of  the  temperature  of  water  at  great  depths  are  self- 
registering  thermometers  either  of  Six's  or  Phillips'  con- 
struction,  inclosed  in  a  glass-case,  hermetically  sealed,  con- 
taining air  and  a  little  alcohol.  The  glass-case  and  inclosed 
air  protect  the  bulb  of  the  thermometer  from  the  immense 
pressure  of  the  superincumbent  water,  which  by  compress- 
ing the  bulb  would  force  mercury  into  the  tube,  and  make 
the  reading  too  high.  The  instrument  represented  in  Fig. 
Fig.  194 c.  194,C  was  designed  by  Sir  Wm.  Thomson,  and  is  used  by 

Thomson's  J  J 

Protected    the  Committee  on  Underground  Temperature  appointed 

*'  by  the  British  Association.     A  is  the  protecting  case,  B 

the  Phillips'  thermometer  inclosed  in  it,  and  supported  by  three 

pieces  of  cork  ccc.     A  small  quantity  of  spirit  s  occupies  the  lower 


DEEP-SEA   AND   WELL   THERMOMETERS.  259 

part  of  the  case;  d  is  the  air-bubble  characteristic  of  Phillips' 
thermometer,  and  serving  to  separate  one  portion  of  the  mercurial 
column  from  the  rest.  In  the  figure  this  air-bubble  is  represented  as 
expanded  by  the  descent  of  the  lower  portion  of  mercury,  while  the 
upper  portion  remains  suspended  by  adhesion.  This  instrument  has 
been  found  to  register  correctly  even  under  a  pressure  of  2J  tons  to 
the  square  inch. 

The  use  of  the  spirit  s  is  to  bring  the  bulb  more  quickly  to  the 
temperature  of  the  surrounding  medium. 

Another  instrument,  designed,  like  the  foregoing,  for  ob- 
servations in  wells  and  borings,  is  Walferdins  maximum 
thermometer  (Fig.  196).  Its  tube  terminates  above  in  a  fine 
point  opening  into  a  cavity  of  considerable  size,  which  con- 
tains a  sufficient  quantity  of  mercury  to  cover  the  point 
when  the  instrument  is  inverted.  The  instrument  is  set  by 
placing  it  in  this  inverted  position  and  warming  the  bulb 
until  the  mercury  in  the  stem  reaches  the  point  and  becomes 
connected  with  the  mercury  in  the  cavity.  The  bulb  is  then 
cooled  to  a  temperature  lower  than  that  which  is  to  be  ob- 
served, and  during  the  operation  of  cooling  mercury  enters 
the  tube  so  as  always  to  keep  it  full.  The  instrument  is 
then  lowered  in  the  erect  position  into  the  bore  where  ob- 
servations are  to  be  made,  and  when  the  temperature  of  the 
mercury  rises  a  portion  of  it  overflows  from  the  tube.  To 
ascertain  the  maximum  temperature  which  has  been  experi- 
enced, the  instrument  may  be  immersed  in  a  bath  of  known 
temperature,  less  than  that  of  the  boring,  and  the  amount  of 
void  space  in  the  upper  part  of  the  tube  will  indicate  the 
excess  of  the  maximum  temperature  experienced  above  that  of  the 
bath. 

If  the  tube  is  not  graduated,  the  maximum  temperature  can  be 
ascertained  by  gradually  raising  the  temperature  of  the  bath  till  the 
tube  is  just  full. 

If  the  tube  is  graduated,  the  graduations  can  in  strictness  only 
indicate  true  degrees  for  some  one  standard  temperature  of  setting, 
since  the  length  of  a  true  degree  is  proportional  to  the  quantity  of 
mercury  in  the  bulb  and  tube ;  but  a  difference  of  a  few  degrees  in 
the  temperature  of  setting  is  immaterial,  since  10°  Cent,  would  only 
alter  the  length  of  a  degree  by  about  one  six-hundredth  part. 

190o  Thermograph. — A  much  more  complete  method  of  obtaining 


260  THERMOMETRY. 

a  register  of  the  indications  of  a  thermometer  in  the  absence  of  an 
observer  is  now  adopted  in  the  principal  British  observatories.  It 
consists  in  the  photographic  registration  of  the  height  of  the  mercurial 
column  at  every  instant  during  the  entire  day.  A  sheet  of  sensitized 
paper  is  mounted  on  a  vertical  cylinder  just  behind  the  mercurial 
column,  which  is  also  vertical,  and  is  protected  from  the  action  of 
light  by  a  cover  of  blackened  zinc,  with  the  exception  of  a  narrow 
vertical  strip  just  behind  the  mercurial  column.  A  strong  beam  of 
light  from  a  lamp  or  gas  flame  is  concentrated  by  a  cylindric  lens,  so 
that  if  the  thermometer  were  empty  of  mercury  a  bright  vertical 
line  of  light  would  be  thrown  on  the  paper.  As  this  beam  of  light 
is  intercepted  by  the  mercury  in  the  tube,  which  for  this  purpose  is 
made  broad  and  flat,  only  the  portion  of  the  paper  above  the  top  of 
the  mercurial  column  receives  the  light,  and  is  photographically 
affected.  The  cylinder  is  made  to  revolve  slowly  by  clock-work,  and 
if  the  mercury  stood  always  at  the  same  height,  the  boundary  between 
the  discoloured  and  the  unaffected  parts  of  the  paper  would  be  straight 
and  horizontal,  in  consequence  of  the  horizontal  motion  of  the  paper 
itself.  In  reality,  the  rising  and  falling  of  the  mercury,  combined 
with  the  horizontal  motion  of  the  paper,  causes  the  line  of  separation 
to  be  curved  or  wavy,  and  the  height  of  the  curve  above  a  certain 
datum-line  is  a  measure  of  the  temperature  at  each  instant  of  the 
day.1  The  whole  apparatus  is  called  a  thermograph,  and  apparatus 
of  a  similar  character  is  employed  for  obtaining  a  continuous  photo- 
graphic record  of  the  indications  of  the  barometer2  and  magnetic 
instruments. 

V  191.  Metallic  Thermometers. — Thermometers  have  sometimes  been 
constructed  of  solid  metals.  Breguet's  thermometer,  for  example 
(Fig.  197),  consists  of  a  helix  carrying  at  its  lower  end  a  horizontal 
needle  which  traverses  a  dial.  The  helix  is  composed  of  three 
metallic  strips,  of  silver,  gold,  and  platinum,  soldered  together  so  as 
to  form  a  single  ribbon.  The  silver,  which  is  the  most  expansible,  is 
placed  in  the  interior  of  the  helix ;  the  platinum,  which  is  the  least 

1  Strictly  speaking,  the  temperatures  corresponding  to  the  various  points  of  the  curve  are 
not  read  off  by  reference  to  a  single  datum- line,  but  to  a  number  of  datum -lines  which 
represent  the  shadows  of  a  set  of  horizontal  wires  stretched  across  the  tube  of  the  ther- 
mometer at  each  degree,  a  broader  wire  being  placed  at  the  decades,  and  also  at  32°,  52°, 
and  72°. 

In  order  to  give  long  degrees,  the  bulb  of  the  thermometer  is  made  very  large — eight 
inches  long,  and  '4  of  an  inch  in  internal  diameter, — (Greenwich  Observations,  1847.) 

2  See  §  110A. 


METALLIC   THERMOMETERS. 


261 


expansible,  on  the  exterior;  and  the  gold  serves  to  connect  them. 
When  the  temperature  rises,  the  helix  unwinds  and  produces  a 
deflection  of  the  needle;  when  the  temperature  falls,  the  helix  winds 
up  and  deflects  the  needle  in  the  opposite  direction. 

Fig.  198  represents  another  dial-thermometer,  in  which  the  thermo- 
metric  portion  is  a  double  strip  comuosed  of  steel  and  brass,  bent  into 


Fig.  197. — Breguet's  Thermometer. 


Fig.  198.— Metallic  Thermometer. 


a  circular  form.  One  extremity  is  fixed,  the  other  is  jointed  to  the 
shorter  arm  of  a  lever,  whose  longer  arm  carries  a  toothed  sector. 
This  latter  works  into  a  pinion,  to  which  the  needle  is  attached. 

It  may  be  remarked  that  dial-thermometers  are  very  well  adapted 
for  indicating  maximum  and  minimum  temperatures,  it  being  only 
necessary  to  place  on  opposite  sides  of  the  needle  a  pair  of  movable 
indices,  which  could  be  pushed  in  either  direction  according  to  the 
variations  of  temperature. 

Generally  speaking,  metallic  thermometers  offer  great  facilities  for 
automatic  registration. 

In  Secchi's  meteorograph,  for  example,  the  temperature  is  indi- 
cated and  registered  by  the  expansion  of  a  long  strip  of  brass  (about 
17  metres  long)  kept  constantly  stretched  by  a  suitable  weight;  this 
expansion  is  rendered  sensible  by  a  system  of  levers  connected  with 
the  tracing  point.  The  thermograph  of  Hasler  and  Escher  consists  of 
a  steel  and  a  brass  band  connected  together  and  rolled  into  the  form 
of  a  spiral.  The  movable  extremity  of  the  spiral,  by  acting  upon  a 
projecting  arm,  produces  rotation  of  a  steel  axis  which  carries  the 
tracer. 
,  192.  Pyrometers. — Metallic  thermometers  can  generally  be  em- 


262 


THERMOMETRY. 


Pig.  199. — Brongniart's  Pyrometer. 


ployed  for  measuring  higher  temperatures  than  a  mercurial  ther- 
mometer could  bear;  but  there  is  great  difficulty  in  constructing  any 
instrument  to  measure  temperatures  as  high  as  those  of  furnaces. 
Instruments  intended  for  this  purpose  are  called  pyrometers. 

Wedgwood,  the  famous  potter,  invented  an  apparatus  of  this  kind, 
consisting  of  a  gauge  for  measuring  the  contraction  experienced  by  a 

piece  of  baked  clay 
when  placed  in  a  fur- 
nace; arid  Brongni- 
art  introduced  into 
the  porcelain  manu- 
factory at  Sevres 
the  instrument  re- 
presented in  Fig.  199, 
consisting  of  an  iron  bar  lying  in  a  groove  in  a  porcelain  slab,  with 
one  end  abutting  against  the  bottom  of  the  groove,  and  the  other 
projecting  through  the  side  of  the  furnace,  where  it  gave  motion  to 
an  indicator. 

Neither  of  these  instruments  has,  however,  been  found  to  furnish 
consistent  indications,  and  the  only  instrument  that  is  now  relied 
on  for  the  measurement  of  very  high  temperatures  is  the  air-ther- 
mometer. 

^  193.  Differential  Thermometer. — Leslie  of  Edinburgh  invented,  in 
the  beginning  of  the  present  century,  an  ingenious  instrument  which 
enables  us  to  measure  small  variations  of  temperature.  A  column  of 
sulphuric  acid,  coloured  red,  stands  in  the  two  branches  of  a  bent 
tube,  the  extremities  of  which  terminate  in  two  globes  of  equal 
volume  (Fig.  200). 

When  the  air  contained  in  the  two  globes  is  at  the  same  tempera- 
ture, whatever  that  temperature  may  be,  the  liquid,  if  the  instrument 
is  in  order,  stands  at  the  same  height  in  the  two  branches.  This 
point  is  marked  zero.  One  of  the  globes  being  then  maintained  at  a 
constant  temperature,  the  other  is  raised  through,  for  instance,  5  de- 
grees, when  the  column  rises  on  the  side  of  the  colder  globe  up  to  a 
point  a,  and  descends  on  the  other  side  to  a  point  b.  Suppose  the 
space  traversed  by  the  liquid  in  each  branch  to  be  divided  into  10 
equal  parts,  each  part  will  be  equivalent  to  a  quarter  of  a  degree. 
This  division  is  continued  upon  each  branch  on  both  sides  of  zero. 
The  differential  thermometer  is  an  instrument  of  great  sensibility, 
and  enabled  Leslie  to  make  some  very  delicate  investigations  on  the 


THE  DIFFERENTIAL  THERMOMETER. 


2G3 


subject  of  the  radiation  of  heat.  It  is  now,  however,  superseded  by 
the  thermo-pile  invented  by  Melloni.  This  latter  instrument  will  be 
described  in  another  portion  of  this  work.  Rumford's  thermoscope 
(Fig.  201)  is  analogous  to  Leslie's  differential  thermometer.  It  differs 


Fig.  200.— Leslie's  Differential  Thermometer. 


Fig.  201. — Rumford's  Thermoscope 


from  it  in  having  the  horizontal  part  much  longer,  and  the  vertical 
branches  shorter.  In  the  horizontal  tube  is  an  alcohol  index,  which, 
when  the  two  globes  are  at  the  same  temperature,  occupies  exactly 
the  middle. 

The  tube  is  divided  into  equal  parts,  and  the  number  of  divisions 
traversed  by  the  index  is  proportional  very  nearly  to  the  difference 
of  temperature  between  the  two  bulbs. 


CHAPTEE   XX. 


FORMULAE   RELATING  TO   EXPANSION. 

•">    194.  Measure  of  Expansion,  Factor  of  Expansion.  —  When  a  sub- 
stance expands,  so  that  its  volume  changes  from  V  to  V/=V-j-/y,  the 

ratio  7^  is  the  numerical  measure  of  the  expansion  per  unit  volume, 
and  is  usually  called  simply  the  expansion  of  the  substance. 

Another  ratio  which  it  is  frequently  necessary  to  consider,  is  y-,  or 

1  -f  v,  that  is  to  say,  the  ratio  of  the  final  to  the  initial  volume.  This 
may  conveniently  be  called  the  factor  of  expansion,  or  the  expansion 
factor.  If  m  denote  the  expansion,  1  +m  will  be  the  factor  of  ex- 
pansion, and  we  have 

(1) 


195.  Coefficient  of  Expansion.  —  It  often  happens  that  when  the 
temperature  of  a  body  is  increased  by  successive  equal   amounts, 
the  successive  increments  of  volume  are  also  equal.     In  this  case  the 
body  is  said  to  expand  uniformly  between  the  extreme  temperatures, 
and  if  V  denote  the  volume  of  the  body  at  0°  Cent.,  and  V'  its 
volume  at  t°,  then  we  have 

V'=V(l  +  K«);  (2) 

where  K  is  a  constant  number,  called  the  coefficient  of  expansion 
per  degree  Centigrade. 

The  coefficient  of  expansion  per  degree  Fahrenheit  will  be  -§-  of 
this  value  of  K,  and  the  coefficient  of  expansion  for  the  interval 
from  0°  to  100°  C.  (if  the  expansion  be  uniform  through  this  range) 
will  be  100  K. 

196.  It  is  usual  to  employ  the  name  coefficient  of  expansion  to 
denote  the  coefficient  of  expansion  per  degree,  the  thermometric  scale 
referred  to  being  stated  in  the  context. 


CUBIC,    LINEAR,   AND   SUPERFICIAL   EXPANSION.  265 

Example.  The  volume  of  a  glass  vessel  is  450  cubic  inches  at 
0°  C.;  find  its  volume  at  80°  G,  the  coefficient  of  expansion  for  glass 
being  -00002.  By  (1)  we  have 

V  =  450  (1  +  80  x  -00002)  =  45072  cubic  inches. 

X  197.  Cubic,  Linear,  and  Superficial  Expansion.  —  Thus  far  we  have 
considered  only  expansion  of-  volume.  When  a  solid  body  expands, 
we  may  consider  separately  the  increase  of  one  of  the  linear  dimen- 
sions of  the  body;  this  is  called  the  linear  expansion.  Or  we  may 
consider  the  increase  in  area  of  any  portion  of  its  surface,  which  is 
called  the  superficial  expansion;  or  finally,  the  increase  of  volume, 
which  is  called  expansion  of  volume,  or  cubical  expansion.  By 
substituting  the  words  "length"  and  "  surface  "  for  "volume"  in  §  194 
we  obtain  definitions  of  linear  and  superficial  expansion  as  numerically 
expressed,  and  we  can  demonstrate  the  two  following  propositions:  — 

(1.)  The  cubical  expansion  is  three  times  the  linear  expansion. 

(2.)  The  superficial  expansion  is  twice  the 
linear  expansion. 

Suppose  Fig.  202  to  represent  a  cube  formed 
of  any  substance,  and  let  the  length  of  each  edge 
of  the  cube  be  unity  at  zero  ;  the  volume  is  con- 
sequently equal  to  1,  and  the  area  of  any  one 
of  the  faces  is  also  represented  by  1.  If  the  Fig.  202. 

body  be  heated  to  any  temperature  t,  each  of  the 
edges  will  increase  by  a  certain  quantity  I,  and  the  area  of  each  face 
will  become  (l+£)2=l  +  2£  +  Z2,  while  the  volume  of  the  cube  will 
become 


But  as  the  quantity  I,  which  represents  the  linear  expansion,  is 
always  very  small,  we  may,  without  sensible  error,  neglect  its  second 
and  third  powers  in  comparison  with  its  first  power.  We  thus  see 
that  the  increase  in  area  of  one  of  the  faces  of  the  cube  is  sensibly 
equal  to  21,  and  that  the  increase  in  volume  is  sensibly  equal  to  SI, 
which  proves  the  propositions.  These  propositions  evidently  hold 
for  the  coefficients  of  expansion,  so  that  we  may  say  that  the  coeffi- 
cient of  linear  expansion  is  equal  to  one-third  of  the  coefficient  of 
cubical  expansion,  and  to  one-half  of  the  coefficient  of  superficial 
expansion. 

The  above  demonstration  supposes  the  body  to  remain  similar  to 
itself  during  expansion,  which  is  not  the  case  with  bodies  of  a  fibrous 


266  FORMULAE   RELATING  TO   EXPANSION. 

or  laminated  structure,  nor  with  crystals,  except  those  belonging  to 
the  cubic  system. 

0     198.  Various  Formulas.  —  From  equations  (1)  and  (2)  we  may  find 
the  value  of  V  in  terms  of  V,  thus, 


that  is  to  say,  given  the  volume  of  a  body  at  a  certain  temperature, 
the  volume  at  zero  is  found  by  dividing  the  given  volume  by  the 
factor  of  expansion. 

Formulae  (1),  (2),  (3),  and  (4)  are  particular  cases  of  a  more  general 
formula.  Let  V  and  V  be  the  volumes  of  the  same  body  at  tempera- 
tures t  and  t'  respectively,  U  the  volume  at  zero,  K  the  coefficient  of 
expansion,  and  m  and  m  the  respective  expansions  between  0  and  t, 
and  0  and  if.  We  then  have,  by  formulae  (1)  and  (2), 


whence  by  division 

V     1  +  m     l  +  Kt  » 


or  the  volumes  of  the  same  body  at  different  temperatures  are  pro- 
portional  to  the  factors  of  expansion. 

The  above  formulae  are  evidently  applicable  also  to  linear  and  super- 
ficial expansions. 

^  199.  Influence  of  Temperature  upon  Density.  —  As  the  density  of  a 
substance  is  inversely  as  the  volume  occupied  by  unit  mass,  it  follows 
from  last  section  that  the  densities  of  the  same  substance  at  different 
temperatures  are  inversely  as  the  factors  of  expansion,  so  that  if  D, 
D',  D0  denote  the  densities  at  the  temperatures  t,  t',  0,  then 

p-   PQ         D0 

1  +  m 


\-  200.  Correction  of  Specific  Gravity  for  Temperature.  —  Let  d  be  the 
density  of  a  substance  at  temperature  t°  Cent.,  and  c?0  its  density  at 
0°  C.  Also,  let  D  be  the  density  of  water  at  t°  C.,  and  D4  its  density 
at  4°  C.  (the  temperature  of  maximum  density).  Then  if  the  specific 


EXPANSION   OF   GASES.  267 

gravity  of  the  substance  be  computed  by  comparing  its  density  with 
that  of  water  at  the  same  temperature,  as  in  the  ordinary  methods  of 

experimental  determination,  the  specific  gravity  thus  obtained  is  ^, 
and  has  different  values  according  to  the  temperature  at  which  the 
determination  is  made. 

The  specific  gravity  as  commonly  given  in  tables  is  the  value  of 
jj2;  that  is  to  say,  is  the  ratio  of  the  density  of  the  substance  at  0°  C. 
to  that  of  water  at  the  temperature  of  maximum  density.  The  tabular 
specific  gravity  is  easily  derivable  from  the  observed  specific  gravity  D> 

if  the  law  of  expansion  of  the  substance  be  known;  for  if  1  4-771 
be  the  factor  of  expansion  of  the  substance  from  0°  C.  to  t°  C.,  and 
1  +e  the  factor  of  expansion  of  water  from  4°  C.  to  t*  C.,  then 


Hence, 


'-0  =  --  17?   or  the  correcting  factor  required  is  -- 
D4     Dl+e  l  +  e 


In  the  case  of  solid  bodies  this  correction  is  generally  of  little  im- 
portance; but  in  determining  the  specific  gravities  of  liquids,  espe- 
cially those  which  are  very  expansible  by  heat,  it  cannot  be  neglected. 
X  201.  Formulae  for  the  Expansion  of  G-ases.  —  The  volume  of  a  gas 
depends  both  on  the  temperature  and  on  the  pressure  to  which  it  is 
subjected;  hence  the  formulae  of  expansion  for  this  class  of  bodies  are 
somewhat  more  complicated.  Suppose  we  wish  to  find  the  relation 
between  the  volumes  V  and  V  of  the  same  mass  of  gas  at  tempera- 
tures t  and  t',  and  under  pressures  P  and  Pf  respectively.  Let  U  be 
the  volume  of  the  given  mass  of  gas  at  pressure  P  and  temperature 
ift  and  let  a  be  the  coefficient  of  expansion  of  the  gas. 

The  two  volumes  V  and  U,  being  under  the  same  pressure,  are 
proportional  to  the  expansion  factors  corresponding  to  their  tempera- 
tures (§  198),  which  gives 


_ 
TJ     l+af' 

The  volumes  U  and  V,  at  the  same  temperature  t',  are,  by  Boyle's 
law,  inversely  proportional  to  the  pressures  ;  whence  we  have 

U  _P' 
V'~p- 

From  these  two  equations  we  obtain  by  multiplication 


208  FORMULA  RELATING  TO   EXPANSION. 


_  ™ 

V7"? 


which  means  that  the  volumes  assumed  by  the  same  mass  of  gas  are 
inversely  proportional  to  the  pressures,  and  directly  proportional 
to  the  expansion  factors  corresponding  to  the  temperatures. 

From  equation  (9)  we  may  easily  deduce  another  equation,  by 
remarking  that  the  densities  of  the  same  quantity  of  gas  must  be 
inversely  as  the  volumes  occupied.  Thus  we  have 

D      P    l  +  atf 


IX     F    1  +  at' 


(10) 


which  signifies  that  the  density  of  a  gas  varies  directly  as  the 
sure,  and  inversely  as  the  expansion  factor  corresponding  to  the 
temperature. 


CHAPTEE    XXI. 


EXPANSION   OF  SOLIDS. 


y  202.  Laplace  and  Lavoisier's  Experiments. — Laplace  and  Lavoisier 
determined  the  linear  expansion  of  a  great  number  of  solids  by  the 
following  method. 

The  bar  AB  (Fig.  203)  whose  expansion  is  to  be  determined,  has 
one  end  fixed  at  A,  while  the  other  can  move  freely,  pushing  before 
it  the  lever  OB,  which  is 
movable  about  the  point 
O,  and  carries  a  tele- 
scope whose  line  of  sight 
is  directed  to  a  scale  at 
some  distance.  It  is  evi- 
dent that  a  displacement 
BB'  will  correspond  to  a 
considerably  greater  length 
CC'  on  the  scale,  which  will 
increase  with  the  distance 
of  the  scale  from  the  telescope.  The  ratio  of  CC'  to  BB'  is  equal 
to  the  ratio  of  OC  to  OB,  and  is  the  same  throughout  the  whole 
course  of  experiments.  In  order  to  determine  this  ratio  once  for  all, 
we  have  only  to  measure  the  distance  CC'  on  the  scale  correspond- 
ing to  a  known  displacement  BB'. 

The  apparatus  employed  by  Laplace  and  Lavoisier  is  shown  in  Fig. 
204.  The  trough  C,  in  which  is  laid  the  bar  whose  expansion  is  to 
be  determined,  is  placed  between  four  massive  uprights  of  hewn  stone 
N.  One  of  the  extremities  of  the  bar  rests  against  a  fixed  bar  B', 
firmly  joined  to  two  of  the  uprights;  the  other  extremity  pushes  the 
bar  B,  which  produces  the  rotation  of  the  axis  aa'.  This  axis  carries 
with  it  in  its  rotation  the  telescope  LL',  which  is  directed  to  the 


Fig.  203. 
Principle  of  the  Method  of  Laplace  and  Lavoisier. 


270 


EXPANSION   OF  SOLIDS. 


scale.     The  first  step  is  to  surround  the  bar  with  melting  ice,  and  then 
observe  the  number  on  the  scale  marked  by  the  line  of  sight  of  the 


Fig.  204. — Apparatus  of  Laplace  and  Lavoisier. 

telescope.     The  temperature  of  the  trough  is  then  raised,  and  the 
corresponding  increase  of  length  is  measured. 

Laplace  and  Lavoisier  have  discovered  by  this  means  that  the 
expansion  of  solids  is  sensibly  uniform  between  0°  and  100°  G;  above 
this  latter  point  it  varies  with  the  temperature. 

The  following  table  contains  the  most  important  results  obtained 
by  them : — 

COEFFICIENTS  OF  LINEAR  EXPANSION. 


Gold,  Paris  standard,  annealed,  0'000015153 
„  „  unannealed,  0*000015515 

Steel  not  tempered,  .  .  .  0-000010792 
Tempered  steel  reheated  to  65°,  0'000012395 
Silver  obtained  by  cupellation,  -0-000019075 
Silver,  Paris  standard,  .  ,  0'000019086 

Copper, 0-000017173 

Brass, 0'000018782 

Malacca  tin, 0*000019376 

Falmouth  tin,    .     .     .     ,      ,     0'000021729 


I    Soft  wrought  iron,       .     . 
Round  iron,  wire  drawn, 
(  English  flint-glass,      .     . 
Gold,  procured  by  parting, 

Platina, 

Lead, 

French  glass  with  lead,   . 

Sheet  zinc, 

Forged  zinc,       .... 


0-000012204 
0-000012350 
0-000008116 
0-000014660 
0-000009918 
0-000088483 
0-000008715 
0-000029416 
0-000031083 


A  simpler  and  probably  more  accurate  method  of  observing  expan- 
sions was  employed  by  Kamsden  and  Roy.  It  consists  in  the  direct 
observation  of  the  distance  moved  by  either  end  of  the  bar,  by  means 
of  two  microscopes  furnished  with  micrometers,  the  microscopes 
themselves  being  attached  to  an  apparatus  which  is  kept  at  a  constant 
temperature  by  means  of  ice. 
4  S03.  Compensating  Pendulum. — The  pendulum,  as  we  know,  regu- 


COMPENSATING   PENDULUM. 


271 


lates  the  motion  of  a  clock.  Suppose  the  clock  to  keep  exact  time 
at  the  temperature  of  zero;  then  if  the  temperature  rises  the  length 
of  the  pendulum  will  increase,  and  with  it  the  duration  of  each  oscilla- 
tion, so  that  the  clock  will  lose.  The  opposite  effect  would  be  pro- 
duced by  a  fall  of  the  temperature  below  zero.  We  thus  see  that 
clocks  are  liable  to  go  too  fast  in  winter,  and  too  slow  in  summer, 
and  that  we  must  move  the  bob  of  the  pendulum  from  time  to  time 
in  order  to  insure  their  regularity. 

The  effect  of  temperature  may  be  notably 
diminished  by  means  of  compensating  pendu- 
lums, of  which  there  are  several  different 
kinds. 

1.  Harrisons  Gridiron  Pendulum. — This 
consists  of  four  oblong  frames,  the  uprights  of 
which  are  alternately  of  steel  F  and  of  brass 
C  (Fig.  205);  the  brass  uprights  rest  upon 
the  bottom  of  the  steel 

frames,  and  to  the  top      ( I i 

of  the  second  brass 
frame  is  attached  the 
steel  rod  carrying  the 
bob.  From  this  ar- 
rangement it  follows 
that  the  effect  of  the 
lengthening  of  the  steel 
rods  will  be  to  lower 
the  bob,  while  that  of 
the  lengthening  of  the 
brass  rods  will  be  to 
raise  it.  It  will  be  seen 
that  these  two  effects 
may  be  made  com- 
pletely to  neutralize 
each  other;  we  have 

!       ,       .  ,  T      ,     , ,  Fig.  205.  Fig-  206. 

Only  tO  insure   that    the      plan  Qf  Gridiron  pendulum.  Gridiron  Pendulum. 

whole  expansion  of  the 

steel  shall  be  equal   to  that  of  the  brass.1      If  L  and  I/  be  the 

1  As  the  weight  of  the  frame  cannot  be  altogether  neglected,  and  the  change  of  dimen- 
sions produced  by  expansion  affects  the  moment  of  inertia,  the  condition  of  compensation 
stated  in  the  text  can  only  be  taken  as  approximate. 


272 


EXPANSION   OF   SOLIDS. 


sum  of  the  lengths  of  the  steel  and  brass  rods  respectively;  then 
this  neutralization  will  be  effected  if  LK£=L'K'£,  or  if  LK  =  L'K', 
where  K  and  K'  are  the  respective  coefficients  of  expansion  of  steel 
and  brass. 

From  the  table  on  page  270  we  learn  that  K  is  about  f  K'; 
thus  the  sum  of  the  lengths  of  the  brass  rods  must  be  about  f- 
of  that  of  the  steel  rods.  This  result  shows  that  we  must  have  at 
least  two  brass  frames,  for  with  only  one  the  compensating  effect 
could  not  be  produced,  as  the  length  of  the  steel  rods  would  in  that 
case  be  about  double  that  of  the  brass.  If  we  wish  to  have  only  a 

single  frame  of  each  different 
metal,  we  must  choose  two 
whose  difference  of  expansion 
is  much  more  marked;  such, 
for  instance,  as  iron  and  zinc, 
which  are  employed  in  Jur- 
gensen's  pendulum. 

In  order  that  the  compen- 
sation may  be  complete,  the 
centre  of  oscillation  (§  46) 
must  remain  at  the  same  dis- 
tance from  the  centre  of  sus- 
pension. The  screw  above 
the  bob,  shown  in  Fig.  206, 
enables  us  to  attain  this  end 
by  slightly  raising  or  depress- 
ing the  bob,  and  is  intended 
to  be  used  once  for  all  to  ad- 
just the  pendulum  to  the  pro- 
per rate. 

2.  Grahams  Pendulum. — 
This  consists  of  an  iron  rod 
carrying  at  its  lower  end  a 
frame,  in  which  are  fixed  one 
or  two   glass   cylinders   con- 
taining mercury.     When  the 
temperature  rises  the  length- 
ening of  the  rod  lowers  the  centre  of  gravity  and  centre  of  oscil- 
lation of  the  whole;  but  the  expansion  of  the  mercury  produces  the 
contrary  effect;  and  it  will  readily  be  understood  that  the  quantity 


Fig.  207.— Graham's 
Mercurial  Pendulum. 


Fig.  208. 
Ellicott's  Pendulum. 


COMPENSATING   PENDULUM.  273 

of  mercury  in  the  cylinders  may  be  such  as  to  produce  an  approxi- 
mately perfect  compensation. 

3.  Ellicott's  Pendulum. — This  pendulum,  which  was  invented  in 
England  in  the  last  century,  is  known  in  France  as  Brocot's  pendu- 
lum, and  is  frequently  used  in  small  French  clocks.  The  main  rod 
/  is  of  iron.  Attached  to  a  cross  -bar  at  the  upper  part  of  this  rod  are 
two  brass  rods  cc,  which,  by  means  of  the  levers  a  a  and  the  pins  it, 
attached  to  the  bob,  raise  this  latter  when  the  temperature  rises. 
The  arms  of  the  levers  may  evidently  be  so  chosen  as  to  maintain 
the  centre  of  oscillation  at  an  invariable  distance  from  the  axis  of 
suspension,  by  means  of  the  different  expansive  powers  of  iron  and 
brass. 

204.  Force  of  Expansion  of  Solids. — The  force  of  expansion  is  very 
considerable,  being  equal  to  the  force  necessary  to  compress  the  body 
to  its  original  dimensions.  Thus,  for  instance,  iron  when  heated  from 
0°  to  100°  increases  by  -0012  of  its  original  length.  In  order  to  pro- 
dace  a  corresponding  change  of  length  in  a  rod  an  inch  square,  a 
force  of  about  15  tons  would  be  required.  It  would  be  useless  to 
attempt  to  offer  any  mechanical  resistance  to  a  force  so  enormous; 
the  only  thing  that  can  be  done,  in  the  case  of  structures  in  which 
metals  are  employed,  is  to  arrange  the  parts  in  such  a  manner  that 
the  expansion  shall  not  be  attended  with  any  evil  effects.  Thus,  in 
a  railway,  the  rails  do  not  touch  each  other,  a  small  interval  being 
left  to  allow  room  for  the  variations  of  length.  Iron  beams  employed 
in  buildings  must  have  the  end  free  to  move  forward  without  encoun- 
tering any  obstacles,  which  they  would  inevitably  overthrow.  Sheets 
of  zinc  and  lead  employed  in  roofing,  are  so  arranged  as  to  be  able  in 
a  certain  extent  to  overlap  each  other  on  expansion. 

We  may  further  remark  that  the  expansion  of  metals,  though 
relatively  very  small,  may  practically  become  very  considerable,  if 
the  length  of  metal  which  expands  is  sufficiently  great.  Suppose  we 
take  as  an  instance  the  length  of  railway  from  London  to  Edinburgh, 
which  is  about  400  miles.  The  extreme  variations  of  temperature 
from  winter  to  summer  are  about  50°  C.,  which  would  produce  a 
variation  of  length  amounting  to  400  X  5280  X '00061 =1288  feet. 
The  actual  variation  is  very  considerable,  and  if  the  rails  formed  a 
continuous  line  at  a  certain  temperature,  this  line  would  be  inter- 
rupted or  broken  in  pieces  upon  a  change  of  temperature  occurring 
in  either  direction. 
V  205.  Conversion  of  Heat  into  Work. — In  conclusion,  we  may  remark 

13 


274  EXPANSION   OF   SOLIDS. 

that  heat  when  applied  to  a  bar  of  metal  produces  two  distinct  and 
separate  effects;  one  shown  in  the  rise  of  temperature,  and  the  other 
in  the  increase  of  volume.  We  may  reasonably  suppose  that  if  the 
solid  body  were  heated  under  such  conditions  as  to  preclude  its  expan- 
sion, the  same  quantity  of  heat  would  produce  a  much  greater  ther- 
mometric  effect  than  in  the  former  case.  A  similar  remark  applies  to 
liquids  and  gases,  and  can  be  easily  verified  by  experiment  in  the 
case  of  these  latter.  Here,  then,  is  the  first  instance  of  a  physical 
phenomenon  of  very  frequent  occurrence,  namely,  the  conversion  of 
heat  into  work,  or  reciprocally,  of  work  into  heat.  Whenever  a 
quantity  of  heat  appears  to  be  lost,  the  reason  is  that  a  corresponding 
amount  of  work  is  produced.  If,  on  the  other  hand,  work  is  done  in 
compressing  a  body,  so  as  to  reduce  it  to  the  volume  which  it  would 
occupy  at  a  lower  temperature,  a  rise  of  temperature  is  necessarily 
produced. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 


CHAPTEE    XXII. 


EXPANSION   OF  LIQUIDS. 


/  206.  Relation  between  Real  and  Apparent  Expansion.  —  If  a  vessel 
containing  a  liquid  be  heated,  the  level  of  the  liquid  rises,  in  conse- 
quence of  the  excess  of  the  expansion  of  the  liquid  over  that  of  the 
vessel.  The  observed  increase  of  volume,  not  corrected  for  the  ex- 
pansion of  the  vessel,  is  called  the  apparent  expansion.  It  is  evidently 
less  than  the  real  expansion,  for  if  the  volume  of  the  vessel  had 
remained  the  same,  the  level  would  have  risen  higher. 

The  coefficients  of  real  and  apparent  expansion  are  connected  with 
the  coefficient  of  expansion  of  the  vessel  by  a  very  simple  relation. 

Let  us  take  the  case  of  a  liquid  contained  in  a  vessel  similar  to  a 
thermometer  in  shape,  that  is,  suppose  the  tube  to  be  divided  into 
parts  of  equal  capacity,  and  that  we  know  by  previous  gauging  how 
many  divisions  are  equivalent  to  the  volume  of  the  reservoir. 

Let  no  denote  the  number  of  divisions  occupied  by  the  liquid  at 
zero,  and  nt  the  number  of  divisions  occupied  at  temperature  f. 

Then  ^  is  the  factor  of  apparent  expansion,  and  J  —  1  is  the 
apparent  expansion. 

Let  us,  for  simplicity,  take  for  our  unit  of  volume  the  volume  of  a 
division  at  zero.  Then  if  K  be  the  expansion  of  the  glass,  the  volume 
of  a  division  at  t°  will  be  1  +  K. 

The  volume  of  the  liquid  at  t°  is  nt  of  these  divisions,  and  is  there- 
fore nt(l+K). 

But  if  m  be  the  real  expansion  of  the  liquid,  the  volume  at  t°  is 
(1  +  m)  n0,  since  nQ  is  the  volume  at  zero. 

Hence  we  have 


and 

nt     1  +m 


276  EXPANSION    OF   LIQUIDS. 

That  is,  the  factor  of  apparent  expansion  is  equal  to  the  factor  of 
real  expansion  of  the  liquid  divided  by  that  of  the  vessel.  Denote 
the  factor  of  apparent  expansion  by  1  +  A  . 

Then  since  from  above 

l+m 
1  +  A 

we  have 
whence 


or  since  AK  is  much  smaller  than  either  A  or  K,  and  may  in  general 
be  neglected, 


That  is,  the  real  expansion  of  the  liquid  is  equal  to  the  apparent 
expansion  plus  the  expansion  of  the  vessel;  and  consequently,  the 
coefficient  of  real  expansion  is  equal  to  the  coefficient  of  apparent 
expansion  plus  the  coefficient  of  expansion  of  the  vessel. 
/  207.  Expansion  of  Glass.  —  By  means  of  this  relation  we  can  find 
the  coefficient  of  expansion  of  any  kind  of  glass  ;  we  have  only  to 
measure  the  coefficient  of  apparent  expansion  of  the  mercury  in  a 
thermometer  made  of  this  glass,  and  to  subtract  it  from  the  coefficient 
of  absolute  expansion  of  the  metal,  which,  as  we  shall  see  afterwards, 

is  equal  to  g^.     The  coefficient  of  apparent  expansion  varies  a  little 
according  to  the  quality  of  the  glass  employed;  if  we  take  it  as  ^-— 

which  is  Dulong  and  Petit's  determination  of  its  mean  value,  we  shall 
have  for  the  coefficient  of  expansion  of  glass 


5550  6480"  38700 

1  208.  Expansion  of  any  Liquid. — The  coefficient  of  expansion  of  the 
glass  of  which  a  thermometer  is  composed  being  known,  we  may  use 
the  instrument  to  measure  the  expansion  of  any  liquid.  For  this 
purpose,  the  liquid  whose  coefficient  of  expansion  is  to  be  determined 
is  introduced  into  the  thermometer,  and  the  number  of  divisions  n0 
and  nt  occupied  by  the  liquid  at  the  temperatures  0°  and  t°  respec- 
tively, are  observed.  Then,  if  D,  A,  K,  be  the  coefficients  of  real 
expansion,  of  apparent  expansion,  and  of  expansion  of  the  glass,  each 
reckoned  per  degree  Centigrade,  we  have 

-  —  1=A£,  whence  A  is  known;  and 


PIERRE  S  APPARATUS. 


277 


1  +D=(]  +  A)  (1 +K),  or  D= A  +  K  nearly,  whence  D  is  known. 

M.  Pierre  has  performed  an  extensive  series  of  experiments  by  this 
method  upon  a  great  number  of 
liquids. 

The  apparatus  employed  by 
him  is  shown  in  Fig.  209.  The 
thermometer  containing  the  given 
liquid  is  fixed  beside  a  mercurial 
thermometer,  which  marks  the 
temperature.  The  reservoir  and 
a  small  part  of  the  tube  are  im 
mersed  in  the  bath  contained  in 
the"  cylinder  below.  The  upper 
parts  of  the  stems  are  inclosed  in 
a  second  and  smaller  cylinder,  the 
water  in  which  is  maintained  at  a 
sensibly  constant  temperature  in- 
dicated by  a  very  delicate  thermo- 
meter. 

From  these  experiments  it  ap- 
pears that  the  expansions  of  li- 
quids are  in  general  much  greater 
than  those  of  solids.  Further,  ex- 
pansion does  not  proceed  uni- 
formly, as  compared  with  the 
indications  of  a  mercurial  ther- 
mometer, but  increases  very  perceptibly  as  the  temperature  rises. 
This  is  shown  by  the  following  table : — 


Volume  at  40". 
1-007492 
1-044882 
1-066863 
1-049006 
1-050509 


-f  209.  Maximum  Density  of  Water. — By  applying  the  experimental 
method  just  described  to  the  case  of  water,  we  may  easily  observe 
the  volume  occupied  by  the  same  weight  of  this  liquid  at  different 
temperatures,  and  it  has  thus  been  found  that  this  volume  is  least  at 
4°  Centigrade.  At  this  temperature,  accordingly,  the  density  of  water 
is  a  maximum,  so  that  if  a  quantity  of  water  at  this  temperature  be 


Fig.  209. — Pierre's  Apparatus. 


\ 
Water  

rolume  at  0°. 
1 

Volume  at  10°. 
1-000146 

Alcohol  

1 

1-010661 

Ether 

1 

1-015408 

Bisulphide  of  carbon... 
Wood-  spirit.... 

1 
1 

1-011554 
1-012020 

278 


EXPANSION   OF  LIQUIDS. 


either  heated  or  cooled  it  undergoes  an  increase  of  volume.  This  is 
a  curious  and  unique  exception  to  the  general  law  of  expansion  by 
heat. 

This  anomaly  may  be  exhibited  by  means  of  the  apparatus  repre- 
sented iri  Fig.  210,  which  consists  of  two  thermometers,  one  of 
alcohol,  and  the  other  of  water.  The  reservoir  of  this  latter,  on 
account  of  the  smaller  expansive  power  of  the  liquid,  is  a  long  spiral, 
enveloping  that  of  the  alcohol  thermometer. 
Both  the  reservoirs  are  contained  in  a  metal 
box,  which  is  at  first  filled  with  melting  ice. 
The  two  instruments  are  so  placed,  that  at 
zero  the  extremities  of  the  two  liquid  columns 
are  on  the  same  horizontal  line.  This  being 
the  case,  if  the  ice  be  now  removed,  and  the 
apparatus  left  to  itself,  or  if  the  process  be 
accelerated  by  placing  a  spirit-lamp  below 
the  box,  the  alcohol  will  immediately  be  seen 
to  rise,  while  the  water  will  descend;  and  the 
two  liquids  will  thus  continue  to  move  in 
opposite  directions  until  a  temperature  of 
about  4°  is  attained.  From  this  moment  the 
water  ceases  to  descend,  and  begins  to  move 
in  the  same  direction  as  the  alcohol.  This 
experiment,  although  very  well  adapted  for 
exhibiting  the  phenomenon,  does  not  enable 
us  to  measure  exactly  the  temperature  of 
maximum  density,  since  it  is  the  apparent, 
and  not  the  real,  expansion  of  water  which 

is  thus  observed.  The  following  experiment,  which  is  due  to  Hope, 
is  more  rigorous. 

A  glass  jar  is  employed,  having  two  lateral  openings,  one  near  the 
top  and  the  other  near  the  bottom,  which  admit  two  thermometers 
placed  horizontally.  The  tube  is  filled  with  water,  and  its  middle  is 
surrounded  with  a  frigorific  mixture.  The  following  phenomena  will 
then  be  observed. 

The  lower  thermometer  descends  steadily  to  4°,  and  there  remains 
stationary.  The  upper  thermometer  at  first  undergoes  very  little 
change,  but  when  the  lower  one  has  reached  the  fixed  temperature, 
the  upper  one  begins  to  fall,  reaches  the  temperature  of  zero,  and, 
finally,  the  water  at  the  surface  freezes,  if  the  action  of  the  frigorific 


Fig.  210.— Maximum  Density 
of  Water. 


EXPANSION   OF  WATER. 


279 


Fig.  211. 
Hope's  Experiment. 


mixture  continues  for  a  sufficiently  long  time.     These  facts  admit  of 
a  very  simple  explanation. 

As  the  water  in  the  middle  portion  of  the  tube  grows  colder  its 
densit}'  increases,  and  it  sinks  to  the  bottom. 
This  process  goes  on  till  all  the  water  in 
the  lower  part  of  the  vessel  has  attained  the 
temperature  of  4°.  But  when  all  the  water 
from  the  centre  to  the  bottom  has  attained 
this  temperature,  any  further  cooling  of  the 
water  in  the  centre  fails  to  produce  motion, 
until  needles  of  ice  are  formed.  These  being 
specifically  lighter  than  water,  rise  to  the  sur- 
face, and  thus  produce  a  circulation  which 
causes  the  water  near  the  surface  to  freeze, 
while  that  near  the  bottom  remains  at  the 
temperature  of  4°. 

This  experiment  represents  on  a  small  scale  what  actually  takes 
place  during  winter  in  pools  of  fresh  water.  The  fall  of  temperature 
at  the  surface  does  not  extend  to  the  bottom  of  the  pool,  where  the 
water,  whatever  be  the  external  temperature,  seldom  falls  below  4°. 
This  is  a  fact  of  great  interest,  as  exemplifying  the  close  connection 
of  natural  phenomena,  and  the  manner  in  which  they  contribute  to 
a  common  end.  It  is  in  virtue  of  this  anomaly  exhibited  by  water 
in  its  expansion,  taken  in  conjunction  with  the  specific  lightness  of 
ice  and  the  low  conducting  power  of  water,  that  the  temperature  at 
the  bottom  of  deep  pools  remains  moderate  even  during  the  severest 
cold,  and  that  the  lives  of  aquatic  animals  are  preserved. 

210.  Saline  Solutions. — In  the  case  of  saline  solutions  of  different 
densities,  the  temperature  of  maximum  density  falls  along  with  the 
freezing-point,  and  in  fact  falls  more  rapidly  than  this  latter,  so  that 
for  solutions  containing  a  certain  proportion  of  salt  the  temperature 
of  maximum  density  is  below  the  freezing-point.  In  order  to  show 
this  experimentally,  the  solution  must  be  placed  in  such  circumstances 
as  to  remain  liquid  at  a  temperature  below  its  freezing-point.  This 
is  a  curious  example  of  the  continuity  of  physical  laws,  and  of  the 
restriction  which  must  be  applied  in  physics  to  the  generally  correct 
and  logical  principle  of  final  causes.  For  salt  water  has  a  point  of 
maximum  density,  although  before  that  point  is  reached  congelation 
takes  place.  In  this  instance  the  maximum  density  plays  no  part  in 
the  designs  of  nature,  and  leads  to  no  practical  benefit,  being  simply 


280  EXPANSION   OF   LIQUIDS. 

a  proof  of  the  permanence  of  a  physical  law,  even  when  the  circum- 
stances on  which  its  utility  depended  have  disappeared. 

211.  Law  of  the  Expansion  of  Liquids.  —  As  we  have  shown  above 
(§  208),  the  expansion  of  liquids  does  not  advance  uniformly  with  the 
temperature;  whence  it  follows  that  the  mean  coefficient  of  expansion 
will  vary  according  to  the  limiting  temperatures  between  which  it  is 
taken. 

From  a  general  review  of  the  researches  which  have  been  made  on 
this  subject,  it  appears  that  for  a  great  number  of  liquids  the  mean 
coefficient  of  expansion  increases  uniformly  with  the  temperature. 
If,  therefore,  A  be  the  expansion  from  0  to  t,  we  have 

—  =  a-\-bt,  whence  &=at  +  ltz, 

a  and  b  being  two  constants  specifying  the  expansibility  of  the  given 
liquid. 

For  some  very  expansible  liquids  two  constants  are  not  sufficient, 
and  the  expansion  is  represented  by  the  formula 


We  subjoin  a  few  instances  of  this  class  taken  from  the  work  of 
M.  Pierre:  — 

Alcohol  .....................  A  =  0-0010486  £  +  0-0000017510  t2  +  0-00000000134518  t3 

Ether  .......................  A=0-0015132  t  +  0-0000023592  «2  +0-000000040051  t* 

Bisulphide  of  carbon....  A  =0'0011398  £+0-0000013707  *2  +0'00000019123  ts 

Bromine  ..................  A  =  0'0010382  Z  +  0'0000017114  Z2  +  0*0000000054471  13 

An  examination  of  the  formulae  for  the  different  liquids  which 
have  been  tested,  shows  that  none  of  them  have  a  point  of  maximum 
density  ;  this  property  remains  peculiar  to  water. 

212.  Absolute  Expansion  of  Mercury.  —  The  great  importance  of 
mercury  in  physical  experiments,  especially  in  connection  with  the 
barometer  and  thermometer,  render  it  necessary  to  determine  very 
accurately  the  coefficient  of  expansion  of  this  liquid.  This  determina- 
tion has  been  effected  by  Dulong  and  Petit  by  a  very  ingenious 
method,  in  which  the  observation  of  the  heights  of  liquid  columns  is 
substituted  for  the  measurement  of  volumes,  which  is  always  open 
to  some  uncertainty. 

A  and  B  are  two  tubes  containing  mercury,  and  communicating 
with  each  other  by  a  very  narrow  tube  C  D.  If  the  temperature  of 
the  liquid  be  uniform,  the  mercury  should  stand  at  the  same  height 


EXPANSION   OF  MERCURY.  281 

in  both  branches,  according  to  the  fundamental  law  of  liquids  in 

communicating  vessels.     But  if  the  tube  AC,  for  instance,  be  kept  at 

0°  Cent.,  and  the  temperature  of  BD  be 

raised,  the  density  of  the  heated  liquid  will 

become  less,  and  a  greater  height  will  conse- 

quently be  required  to  equilibrate  the  pres- 

sure of  the  other  column. 

Suppose  the  horizontal  tube  divided  by  a 
vertical  section,  and  let  h  and  h'  denote  the 
respective  heights  of  the  liquid  in  the  cold 
and  in  the  heated  branches  above  the  centre 
of  gravity  of  this  section.  As  the  pressures 
on  both  sides  must  be  equal,  we  must  have 
the  equation  lid  —  h'd',  where  d  and  dr  are 

,  ,         ,          ...  p    ,  ,  ,       ,        Fig.  212.—  Principle  of  Dulong's 

the  densities  of  the  mercury  at  zero  and  at  Method. 

the  other  given  temperature. 

But  from  what  has  been  said  above  (§  199),  we  have  d'=^ 


where  m  is  the  expansion  of  the  liquid  from  0°  to  t°  ;  and  consequently, 
whence 


We  thus  see  that  it  is  sufficient  to  measure  exactly  the  heights  h'  and 
h  in  order  to  find  m. 

We  should  remark,  that  the  centre  of  gravity  of  the  liquid  section 
which  we  have  been  considering,  is  the  only  point  of  it  which  is  in 
equilibrium  ;  the  upper  part  is  subject  to  a  greater  pressure  on  the 
side  of  the  heated  liquid,  and  the  lower  part  on  the  side  of  the  cold  ; 
there  is  thus  a  tendency  to  the  production  of  two  opposite  currents, 
which,  however,  is  almost  completely  destroyed  by  the  smallness  of 
the  bore  of  the  connecting  tube.  Even  supposing  these  currents 
actually  to  exist,  the  inverse  effects  produced  by  them  would  sensibly 
compensate  each  other,  compared  with  the  heights  of  the  liquid  in 
the  two  branches. 

The  following  is  the  method  by  which  Dulong  and  Petit  have 
carried  out  the  above  principle. 

The  connecting  tube,  between  the  two  branches  A  and  B  of  the 
apparatus  (Fig.  213),  rests  upon  a  T-shaped  iron  support,  carrying 
two  spirit-levels  at  right  angles  to  each  other  for  insuring  horizon- 
tality.  One  of  the  branches  B  is  inclosed  in  a  cylinder  containing 


282 


EXPANSION   OF  LIQUIDS. 


melting  ice;  the  other  A  is  surrounded  by  a  copper  cylinder  filled 
with  oil,  and  heated  by  a  furnace  connected  with  the  apparatus.  In 
making  an  observation  the  first  step  is  to  arrange  the  apparatus  so 


Fig.  213.— Apparatus  of  Dulong  and  Petit. 

that,  when  the  oil  is  heated  to  the  temperature  required,  the  mercury 
in  the  tube  A  may  just  be  seen  above  the  top  of  the  cylinder,  so  as 
to  be  sighted  with  the  telescope  of  a  cathetometer ;  this  may  be 
effected  by  adding  or  taking  away  a  small  quantity  of  oil.  The 
extremity  of  the  column  B  is  next  sighted,  which  gives  the  difference 
of  the  heights  h'  and  h.  It  is  further  necessary  to  determine  the 
absolute  height  h. 

For  this  purpose  the  height  of  a  reference  mark  i  above  the  surface 
of  the  T-shaped  support  has  been  directly  measured.  From  this 
height  half  the  external  diameter  of  the  horizontal  tube  is  to  be  sub- 
tracted, and  it  only  remains  to  observe  the  distance  of  the  end  of  the 
column  B  from  the  mark  at  the  time  of  the  experiment. 

The  temperature  of  the  oil  is  given  by  the  weight-thermometer  t, 
and  by  the  air- thermometer  r,  which  latter  we  shall  explain  here- 
after. 

By  means  of  this  method  Dulong  and  Petit  ascertained  that  the 
expansion  of  mercury  is  sensibly  uniform,  as  compared  with  the 


EXPANSION   OF   IRON   AND   PLATINUM.  283 

indications  of  an  air-thermometer,  between  0°  and  1  00°  C.  Above 
this  point  it  goes  on  increasing  like  other  liquids,  but  not  in  any 
marked  degree.  Thus,  the  mean  coefficient  between  0°  and  100°  is 

.     Between  0°  and  200°  it  becomes          and         between  0°  and 


300°. 

Kegnault,  without  altering  the  principle  of  the  experiments  of 
Dulong  and  Petit,  introduced  several  improvements  into  their  appar- 
atus, and  added  greatly  to  the  length  of  the  tubes  A  and  B,  thereby 
rendering  the  apparatus  more  sensitive.  The  results  obtained  by 
him  do  not  differ  very  materially  from  those  of  Dulong  and  Petit  ; 
thus,  for  instance,  he  makes  the  coefficient  between  0°  and  100°  equal 


His  experiments  show  that  the  mean  coefficient  between  0°  and 
50°  is  --,  a  number  almost  identical  with        . 


213.  Expansion  of  Iron  and  Platinum.  —  The  coefficient  of  absolute 
expansion  of  mercury  being  known,  that  of  glass  is  deduced  from  it 
in  the  manner  already 
indicated  (§  207).     Du- 
long   and    Petit    have 
deduced  from  it  also  the 

Coefficients  Of  expansion  Fig.  214.—  Expansion  of  Iron  and  Platinum. 

of  iron   and  platinum, 

neither  of  which  metals  are  attacked  by  mercury.     The  method  em- 

ployed is  the  following. 

The  metal  in  question  was  introduced,  in  the  shape  of  a  cylindrical 
bar,  into  the  reservoir  of  a  weight-  thermometer.  Let  W  be  the 
weight  of  the  metal  introduced,  and  D  its  density  at  zero.  The 
process  is  the  same  as  in  using  the  weight-thermometer;  that  is,  after 
having  filled  the  reservoir  with  mercury  at  0°  C.,  we  observe  the 
weight  w  of  the  metal  which  issues  at  a  given  temperature  t.  The 

volume  at  0°  C.  of  the  mercury  which  has  issued,  is  ^,  d  being  the 
density  of  mercury  at  zero;  the  volume  at  t°  is  therefore  ^  (1  +mf), 

m  being  the  coefficient  of  expansion  of  mercury.  This  volume  evi- 
dently represents  the  expansion  of  the  metal,  plus  that  of  the 
mercury,  'minus  that  of  the  glass.  If  then  M  denote  the  weight  of 
mercury  that  fills  the  apparatus  at  0°  C.,  and  if  K  be  the  coefficient 


284  EXPANSION   OF  LIQUIDS. 

of  cubical  expansion  of  glass,  and  x  the  expansion  of  unit  volume  of 
the  given  metal,  we  have  the  equation 


whence  we  can  find  x. 

214.  Convection  of  Heat  in  Liquids.  —  When  different  parts  of  a 
liquid  are  heated  to  different  temperatures,  corresponding  differences 
of  density  arise,  leading  usually  to  the  formation  of  currents  which 
tend  to  produce  equality  of  temperature  as  far  as  their  presence 
extends.    To  this  phenomenon,  which  is  altogether  distinct  from  con- 
duction, the  name  of  convection  is  given. 

Thus,  for  instance,  if  we  apply  heat  to  the  bottom  of  a  vessel  con- 
taining water,  the  parts  immediately  subjected  to  the  action  of  the 
heat  expand  and  rise  to  the  surface  ;  they  are  replaced  by  colder 
layers,  which  in  their  turn  are  heated  and  ascend;  and  thus  the  pro- 
cess continues  indefinitely.  The  two  currents  can  be  very  well 
shown  by  throwing  some  oak  saw-dust  into  the  water.  By  the 
movements  of  this  substance,  which  has  nearly  the  same  density  as 
water,  it  will  be  seen  that  the  ascending  current  occupies  the  centre 
of  the  vessel,  while  the  descending  current  passes  along  the  sides. 

215.  Heating  of  Buildings  by  Hot  Water.  —  This  is  a  simple  applica- 
tion of  the  principle  just  stated.     One  of  the  most  common  arrange- 
ments for  this  purpose  is  shown  in  Fig.  215;  it  is  called  the  high- 
pressure  system,  because  the  water  in  the  boiler  can  acquire  a  tem- 
perature considerably  above  100°  C.     The  boiler  C  is  heated  by  a 
fire  below  it,  and  the  products  of  combustion  escape  through  the 
chimney  A  B.     At  the  top  of  the  house  is  a  reservoir  D,  communicat- 
ing with  the  boiler  by  a  tube.     From  this  reservoir  the  liquid  flows 
into  another  reservoir  E  in  the  story  immediately  below,  thence  into 
another  reservoir  F,  and  so  on.     Finally,  the  last  of  these  reservoirs 
communicates  with  the  bottom  of  the  boiler.     The  boiler,  tubes,  and 
reservoirs  are  all  completely  filled  with  water,  with  the  exception  of 
a  small  space  left  above  in  order  to  give  room  for  the  expansion  of 
the  liquid.     An  ascending  current  flows  through  the  left-hand  tube, 
and  the  circulation  continues  with  remarkable  regularity,  so  long  as 
the  temperature  of  the  water  in  the  boiler  remains  constant. 

216.  Currents  in  the  Sea.  —  In  the  production  of  these  currents 
convection  plays  an  important,  though  perhaps  not  the  principal  part. 
In  fact,  the  sea  is  an  enormous  mass  of  liquid  whose  temperature 
varies  from  point  to  point     Equilibrium  is  consequently  impossible, 


CUKRENTS   IN   THE  SEA. 


285 


and  the  different  parts  must  therefore  be  in  a  state  of  continual 
motion  with  regard  to  each  other.  The  waters  of  the  tropical  seas 
should,  by  reason  of 
their  excess  of  tempera- 
ture, have  a  higher  level 
than  those  of  the  polar 
seas;  and  the  result  is, 
a  continual  kind  of 
overflowing  of  the  wa- 
ters about  the  equator, 
and  consequently  a  vast 
current  setting  towards 
the  poles.  But  to  this 
current  evidently  cor- 
responds a  lower  current 
of  cold  water  flowing 
towards  the  equator, 
there  to  become  heated, 
to  overflow  again,  and 
so  on.  One  of  the  most 
remarkable  of  oceanic 
currents  is  that  which 
is  known  as  the  Gulf 
Stream.  This  current 
of  warm  water  forms  a 
kind  of  immense  river 
in  the  midst  of  the  sea, 
differing  in  the  tern 
perature,  saltness,  and  colour  of  its  waters  from  the  medium  in  which 
it  flows.  Its  origin  is  in  the  Gulf  of  Mexico,  whence  it  issues  through 
the  straits  between  the  Bahamas  and  Florida,  turns  to  the  north- 
west, and  splits  into  two  branches,  one  of  which  goes  to  warm  the 
coasts  of  Ireland  and  Norway,  the  other  gradually  turns  southwards, 
traverses  the  Atlantic  from  north  to  south,  and  finally  loses  itself  in 
the  regions  of  the  equator. 

"The  Gulf  Stream  is  a  river  in  the  ocean;  in  the  severest  droughts 
it  never  fails,  and  in  the  mightiest  floods  it  never  overflows;  its 
banks  and  its  bottom  are  of  cold  water,  while  its  current  is  of  warm ; 
it  takes  its  rise  in  the  Gulf  of  Mexico,  and  empties  into  Arctic  seas. 
There  is  on  earth  no  other  such  majestic  flow  of  waters.  Its  current 


Fig.  215.— Heating  by  Hot  Water. 


286  EXPANSION   OF   LIQUIDS. 

is  more  rapid  than  the  Mississippi  or  the  Amazon,  and  its  volume 
more  than  a  thousand  times  greater.  Its  waters,  as  far  out  from  the 
Gulf  as  the  Carolina  coasts,  are  of  indigo  blue.  They  are  so  distinctly 
marked  that  their  line  of  junction  with  the  common  sea- water  may 
be  traced  by  the  eye.  Often  one-half  of  the  vessel  ma}^  be  perceived 
floating  in  Gulf  Stream  water,  while  the  other  half  is  in  common 
water  of  the  sea,  so  sharp  is  the  line." — (Maury,  Physical  Geography 
of  the  Sea.) 

Another  cause  of  oceanic  currents  is  to  be  found  in  the  winds, 
which  again  are  themselves  examples  of  convective  currents  in  the 
atmosphere.  In  the  case  of  the  Gulf  Stream,  it  would  appear  that 
an  accumulation  of  water  is  produced  in  the  Gulf  of  Mexico  by  the 
trade- wind  which  blows  steadily  towards  it  over  the  South  Atlantic. 
The  elevation  of  level  occasioned  by  this  accumulation  is  probably  to 
be  regarded  as  the  principal  cause  of  the  Gulf  Stream.  We  shall 
discuss  the  origin  of  winds  in  a  later  chapter  (Chap,  xxxiv.) 


CHAPTER    XXIII. 


EXPANSION   OF  GASES. 


217.  Experiments  of  Gay-Lussac. — Gay-Lussac  conducted  a  series  of 
researches  on  the  expansion  of  gases,  the  results  of  which  were  long 
regarded  as  classical.  He  employed  a  thermometer  with  a  large 
reservoir  A,  containing  the  gas  to  be  operated  on;  an  index  of  mer- 
cury mn  separated  the  gas  from  the  external  air,  while  leaving  it 
full  liberty  to  expand.  The  gas  had  previously  been  dried  by  pass- 


Fig.  216.— Gay-Lussac' s  Apparatus. 

ing  it  through  a  tube  containing  chloride  of  calcium,  or  some  other 
desiccating  substance.  The  thermometer  was  fixed  in  a  vessel  which 
was  first  filled  with  melting  ice,  and  when  the  gas  had  thus  been 
brought  to  0°  C.,  the  tube  was  so  adjusted  that  the  index  coincided 
with  the  opening  through  which  the  thermometer  passed. 

The  tube  being  divided  into  parts  of  equal  capacity,  and  the  re-    A-O-V) 
servoir  having  been  previously  gauged,  the  volume  V  is  known  which 
is  occupied  by  the  gas  at  an  external  pressure  H  indicated  by  a  baro- 
meter; the  apparatus  is  then  raised  to  a  given  temperature  T  by 


288  EXPANSION   OF   GASES. 

means  of  the  furnace  below  the  vessel,  and  the  stem  of  the  thermo- 
meter is  moved  until  the  index  reaches  the  edge  of  the  opening ;  at 
this  new  temperature  the  gas  occupies  a  volume  V'  expressed  in 
divisions  of  the  tube:  at  the  same  time  the  pressure  may  have  varied; 
suppose  it  to  have  become  H'.  From  these  data  it  is  easy  to  deduce 
the  expansion  of  unit  volume  of  the  gas  from  0°  to  T  at  constant 
pressure.  If  D  denote  this  expansion,  the  volume  of  the  gas  at  T  at 
the  original  pressure  would  be  V  (1+D).  But  the  gas  occupies  a 
volume  V  at  the  temperature  T  and  pressure  H'.  At  the  pressure 

TT/ 

H  the  volume  would  therefore  be  V'  -jj.     But  the  divisions  of  the 

thermometer  have  expanded  in  the  ratio  1+KT,  K  being  the  co- 
efficient of  expansion  of  glass :  the  true  expression  therefore  for  the 

/•  ,t                                      TT  •    V(1  +  KT)H'       , 
new  volume  of  the  gas  at  the  pressure  H  is    -*— -g ;  whence  we 

have  the  equation 

H' 

V(1  +  D)  =  V'(1+KT)H» 

from  which  we  can  find  the  value  of  D,  and  consequently  that  of  the 
mean  coefficient  of  expansion  ^r.  By  means  of  this  method  Gay- 

Lussac  arrived  at  the  following  results : — 

1st. — All  gases  expand  by  the  same  amount  between  the  same 
limits  of  temperature. 

2d. — The  coefficient  of  expansion  is  independent  of  the  pressure. 
He  also  found  that  the  coefficient  of  expansion  of  air  between  0°  and 
100°  was  -00375. 

These  laws,  which,  together  with  Boyle's  law,  were  long  regarded 
as  defining  the  fundamental  properties  of  the  gaseous  state,  are  not 
rigorously  exact,  but  are  subject  to  restrictions  similar  to  those 
which  apply  to  Boyle's  law.  The  absolute  value  of  the  co-efficient 
of  expansion  of  air  as  laid  down  by  Gay-Lussac  is  very  sensibly 
erroneous.  The  true  value  has  been  determined,  by  subsequent  ex- 
periments conducted  with  greater  precision,  to  be  '003665,  or  ^ 

218.  Regnault's  Experiments. — The  apparatus  employed  by  Gay- 
Lussac  had  one  serious  imperfection.  The  mercurial  index  did  not 
constitute  a  sufficient  barrier  between  the  gas  under  investigation  and 
the  external  air;  so  that  a  portion  of  the  gas  was  able  to  escape,  while 
at  the  same  time  some  of  the  external  air  became  mixed  with  the  gas; 
either  of  which  circumstances  would  impair  the  accuracy  of  the  ex- 
periment. It  also  appears  that  the  means  employed  by  Gay-Lussac 


REGNAULT  S   APPARATUS. 


289 


for  desiccating  the  gas  were  insufficient.  However  this  may  be,  the 
subject  of  the  expansion  of  gases  has  been  taken  up  by  several  phy- 
sicists, as  Pouillet,  Rudberg,  Magnus,  and  Regnault,  who  have  per- 
formed a  number  of  experiments  on  this  subject,  of  undoubted  ac- 
curacy, the  result  of  which  has  been  slightly  to  modify  the  conclusions 
arrived  at  by  Gay-Lussac. 

We  shall  confine  ourselves  to  describing  one  of  the  methods  em- 
ployed by  Regnault. 

The  apparatus  consists  of  a  glass  ball  with  a  narrow  neck,  contain- 
ing the  gas.  This  is  placed  in  a  boiler  (Fig.  217),  containing  water, 


Fig.  217.— Regnault's  Apparatus. 

which  can  afterwards  be  raised  to  ebullition.  A  T-shaped  tube, 
with  three  branches,  establishes  communication  between  the  neck  of 
the  globe  and  a  S3^stem,  consisting  of  two  tubes,  containing  mer- 
cury, and  forming  in  fact  a  mercurial  manometer,  and  also  between 

the  globe  and  a  series  of  desiccating  tubes,  not  shown  in  the  figure, 

19 


290  EXPANSION   OF  GASES. 

which  are  themselves  in  communication  with  a  small  air-pump.  On 
the  first  branch  of  the  manometer,  near  the  capillary  portion  of  the 
tube,  is  a  reference  mark. 

The  following  is  the  mode  of  determining  by  means  of  this  ap- 
paratus the  coefficient  of  expansion  between  0°  and  100°  C.  The 
first  step  is  to  exhaust  the  globe  a  certain  number  of  times,  each  time 
refilling  it  with  air,  or  with  the  gas  under  investigation,  which  has 
been  dried  by  passing  it  through  the  desiccating  tubes.  The  drying 
may  be  rendered  more  complete  and  rapid  by  raising  the  temperature 
of  the  globe.  This  series  of  operations  is,  as  Regnault  has  shown, 
absolutely  necessary  in  order  to  remove  from  the  surface  of  the  glass 
the  last  traces  of  moisture,  which  are  exceedingly  tenacious. 

The  gas  having  been  admitted  for  the  last  time,  the  globe  is  sur- 
rounded with  melting  ice,  and  is  left  to  itself.  The  gas  contracts,  and 
a  fresh  portion  enters  the  globe,  having  first  been  perfectly  dried  by 
passing  through  the  desiccating  tubes.  The  apparatus  is  thus  filled 
with  gas,  and  communication  is  established  for  a  few  seconds  with  the 
external  air,  so  that  the  gas  is  at  atmospheric  pressure.  Mercury  is 
then  poured  into  the  manometer  so  as  to  bring  the  level  of  the  fluid, 
which  is  the  same  in  both  branches,  up  to  the  reference  mark.  The 
branch  of  the  T  which  established  communication  between  the  globe 
and  the  desiccating  tubes  is  then  hermetically  sealed  by  directing 
the  flame  of  a  blowpipe  upon  it. 

The  effect  of  this  operation  has  thus  been  to  isolate  a  quantity  of 
gas  at  the  atmospheric  pressure  H.  This  quantity  consists  of  — 

(J.)  A  volume  V  at  the  temperature  of  0°  C.,  V  being  the  known 
volume  of  the  globe. 

(2.)  A  volume  v,  which  is  very  small,  extending  from  the  neck  of 
the  crlobe  to  the  mark  on  the  manometric  tube.  This  volume  v  is  at 

O 

the  surrounding  temperature  t't  if  brought  to  zero,  it  would  become 
j—-^,  «  being  the  coefficient  of  expansion  of  the  gas.  In  the  first 

part  of  the  experiment,  therefore,  we  have  a  quantity  of  gas  which, 
when  reduced  to  the  temperature  of  zero  and  pressure  H,  would  have 
the  volume 


The  ice  surrounding  the  globe  is  now  removed,  the  boiler  is  filled 
with  water,  which  is  heated  to  ebullition  ;  the  volume  and  pressure 
of  the  gas  increase,  the  mercury  consequently  falls  in  the  first  branch 
of  the  manometer,  and  rises  in  the  other.  When  equilibrium  of  tern- 


THE   COEFFICIENT   OF   EXPANSION.  291 

perature  has  been  established,  mercury  is  poured  into  the  open 
branch,  so  as  to  raise  that  in  the  other  branch  to  the  mark.  There 
is  then  found  to  be  a  difference  of  level  h  :  the  external  pressure  may 
have  changed  at  the  same  time,  and  become  IF;  the  gas  is  conse- 
quently subjected  to  a  pressure  H'  +  /L  Its  volume  consists  of  two 
parts:  — 

(1.)  The  volume  V  (1  +KT)  of  the  globe,  K  denoting  the  coefficient 
of  expansion  of  the  glass,  and  T  the  temperature  of  the  boiling  water 
at  the  moment  of  the  experiment  ;  this  volume  when  reduced  to  zero 

becomes 

vq+KT) 

1  +  aT     ' 

(2.)  The  volume  v  of  the  tube  as  far  as  the  mark,  which  volume  at 
zero  becomes  ;  —  p,  where  t'  is  the  surrounding  temperature.  Thus, 

in  the  second  part  of  the  experiment,  the  given  quantity  of  gas  under 
the  pressure  H'+'i,  would,  at  the  temperature  of  zero,  occupy  the 

volume 

V_(1+KT)  v 

1  +  aT  ~ 


We  have  thus,  by  expressing  that  the  volumes  are  inversely  as 
the  pressures, 


whence 


_    __ 

l  +  at      H'  +  A  ~l  +  at' 


To  solve  this  equation  we  have  recourse  to  a  method  frequently 
employed  in  physics,  which  is  called  the  method  of  successive  ap- 
proximations; v  being  a  very  small  quantity,  is  at  first  supposed  to 
be  zero  ;  on  this  supposition  the  value  of  a  is  easily  obtained.  This 

value  is  then  substituted  in  the  correcting  terms  Y+M*  ITo?'  wnence 
the  real  value  of  aT  is  deduced.  Now  T  is  the  temperature  at  which 
the  water  boils,  and  is  always  known,  as  we  shall  see  hereafter,  if 
the  external  pressure  is  known. 

In  the  experiment  just  described,  the  volume  of  the  gas  remains 
sensibly  the  same,  and  the  effect  of  heat  is  shown  by  an  increase  of 
pressure.  We  might  have  proceeded  differently,  and  caused  the  gas 
to  expand  under  a  constant  pressure. 

We  shall  not  stop  to  describe  the  modified  form  of  the  apparatus 


292  EXPANSION   OF  GASES. 

which  is  adapted  to  this  other  mode  of  experiment;  we  shall  only 
remark  that  the  results  obtained  by  the  two  processes  do  not  exactly 
agree,  as  will  be  seen  from  the  following  table: — 

COEFFICIENTS  OF  EXPANSION  PER  DEGREE  CENTIGRADE. 

From  experiments  at  From  experiments  at 

constant  volume.  constant  pressure. 

Air 0-003665  0*003670 

Nitrogen 0*003668  

Hydrogen 0*003667 0*003661 

Carbonic  oxide 0'003667  0*003669 

Carbonic  acid 0'003688  0*003710 

Nitrous  oxide 0*003676 0*003720 

Cyanogen 0*003829  0*003877 

Sulphurous  acid 0*003845  0*003903 

This  table  shows  that  each  gas  has  its  own  coefficient  of  expansion, 
as  we  have  already  seen  that  each  has  its  own  coefficient  of  com- 
pressibility. Non-liquefiable  gases,  however,  have  nearly  the  same 
coefficient  of  expansion,  a  result  which  accounts  for  the  conclusion 
arrived  at  by  Gay-Lussac. 

As  regards  the  differences  between  the  two  sets  of  numbers,  it  is  to 
be  noted  that  the  second  set  alone  represent  expansion  as  directly 
observed.  The  first  set  directly  measure  the  increase  of  pressure 
which  occurs  when  expansion  is  prevented.  If  Boyle's  law  were  rigor- 
ously true,  the  two  sets  of  results  ought  to  be  identical.  In  point  of 
fact,  it  will  be  remarked  that,  except  in  the  case  of  hydrogen,  the 
numbers  in  the  second  column  are  larger  than  those  in  the  first, 
indicating  that  the  product  of  volume  and  pressure  diminishes 
slightly  as  the  pressure  increases. 

We  may  add  that  the  coefficient  of  expansion  increases  very  sensi- 
bly with  the  pressure;  thus,  between  the  pressures  of  one  and  of 
three  atmospheres  the  coefficient  of  expansion  of  air  varies  from 
0-00367  to  0-00369.  This  increase  is  still  more  marked  in  the  case  of 
liquefiable  gases. 

The  coefficient  of  expansion  per  degree  Fahrenheit  is  |-  of  the 
coefficient  per  degree  Centigrade.  For  air  or  any  non-liquefiable  gas 
this  may  be  taken  as  '002036  or  ^T. 

219.  Air-thermometer.—- We  have  already  stated,  in  connection 
with  the  mercurial  thermometer,  that  the  name  degree  (Centigrade) 
is  given  to  the  hundredth  part  of  the  apparent  expansion  of  the 
mercury  in  the  glass.  As  the  different  kinds  of  glass  employed  in 
the  construction  of  these  instruments  have  not  the  same  law  of 


AIR-PYROMETER.  293 

expansion,  it  follows,  as  we  have  remarked,  that  mercurial  thermo- 
meters are  not  rigorously  comparable  with  each  other,  particularly 
above  100°. 

The  expansion  of  air  being  much  more  considerable  than  that  of 
mercury,  the  variations  caused  by  differences  in  the  glass  will  be 
relatively  less ;  for  this  reason  (as  well  as  for  others  which  will  be 
stated  hereafter)  the  air-therrnometer  is  employed  to  measure  tem- 
perature in  experiments  of  precision. 

Any  apparatus  that  will  measure  the  expansion  of  air  may  serve 
as  an  air-thermometer;  we  have  only  to  consider  T  as  the  unknown 
quantity  in  the  expression  1+aT,  writing  for  a  the  value  of  the 
coefficient  of  expansion  given  in  last  section. 

M.  Pouillet  proposed  to  employ  air  in  pyrometric  investigations, 
and  constructed  an  instrument  to  which  he  gave  the  name  of  air- 
pyrometer,  and  with  which  he  performed  some  interesting  experi- 
ments. Pouillet's  pyrometer  was  very  similar  to  Regnault's  apparatus 
described  above  (§  218);  but  the  reservoir  and  part  of  the  tube  were 
of  platinum,  so  as  to  be  able  to  resist  high  temperatures.  The  indica- 
tions of  this  instrument,  however,  could  not  be  entirely  relied  on, 
since  platinum  has  the  property  of  condensing  air  upon  its  surface, 
and  partially  giving  it  out  at  high  temperatures.  At  such  tempera- 
tures, also,  platinum  becomes  quite  permeable  to  some  of  the  gases 
of  the  furnace.  For  pyrometric  purposes  it  is  better  to  inclose  the 
air  in  a  porcelain  vessel,  as  has  been  done  by  Deville  and  Troost.1 

219A.  Absolute  Temperature.  Absolute  Zero. — If  the  air-thermo- 
meter be  made  the  standard  of  temperature,  equal  differences  of  tem- 
perature will  correspond  to  equal  differences  in  the  volume  occupied 
by  a  given  mass  of  air  at  constant  pressure,  the  difference  amounting 
to  ^7-5-  of  the  volume  at  0°  C.  for  each  degree  Centigrade,  or  to  T£T 
of  the  volume  at  32°  F.  for  each  degree  Fahrenheit. 

1  The  following  account  of  a  pyrometer  constructed  by  Regnault,  on  the  principle  of  the 
air-thermometer,  is  given  in  Dr.  B.  Stewart's  treatise  on  heat.  "  There  is  a  kind  of  flask, 
either  cylindrical  or  spherical,  which  may  be  either  of  cast  or  wrought  iron,  of  platinum  or 
of  porcelain:  the  mouth  is  closed  by  a  plate  containing  a  small  aperture.  From  15  to  20 
grammes  of  mercury  are  added  to  this  flask,  which  is  then  placed  in  that  part  of  the  furnace 
the  temperature  of  which  we  desire  to  know.  The  mercury  soon  boils,  its  vapour  expels 
the  air  by  the  orifice,  and  the  excess  of  mercurial  vapour  goes  off  by  the  same  means. 
When  the  apparatus  has  acquired  the  temperature  of  the  furnace  the  flask  is  withdrawn 
and  made  to  cool  rapidly,  and  the  mercury  which  remains  in  the  flask  is  weighed.  It  may 
be  weighed  directly,  or  if  it  contains  impurity,  it  is  dissolved  in  acid,  and  estimated  as  a 
precipitate.  This  weight  is  that  of  the  vapour  of  mercury  which  filled  the  flask  at  the 
temperature  of  the  furnace,  and  the  volume  of  the  flask,  as  well  as  the  density  of  mercurial 
vapour  being  known,  this  temperature  may  thus  be  determined." 


294*  EXPANSION    OF   GASES. 

The  lowest  temperature  that  could  thus  be  expressed  is  evidently 
—273°  C.  or  —459°  F.,  since  at  this  temperature  the  given  mass  of  air 
would  be  reduced  to  a  mathematical  point.  This  is  often  called  the 
absolute  zero  of  temperature,  and  temperatures  reckoned  from  it  are 
called  absolute  temperatures. 

If  C  and  F  denote  temperatures  Cent,  and  Fahr.  respectively, 
273  +  C  and  459  +  F  will  be  the  corresponding  expressions  for  absolute 
temperature. 

The  statement  of  the  relations  between  the  volume,  pressure  and 
temperature  of  a  given  mass  of  air  or  other  gas  can  be  somewhat 
simplified  by  the  employment  of  this  term.  These  relations  (assum- 
ing the  correctness  of  Boyle's  and  Gay-Lussac's  laws)  are  as  follows  :— 

1.  The  volume  varies  directly  as  the  absolute  temperature,  when 
the  pressure  is  constant. 

2.  The  pressure  varies  directly  as  the  absolute  temperature,  when 

the  volume  is  constant. 

VP 

3.  For  all  variations,  the  expression  -^  remains  constant  in  value, 

V  denoting  volume,  P  pressure,  and  T  absolute  temperature. 

The  subject  of  this  section  will  be  further  discussed  in  Chap, 
xxxii. 

220.  Density  of  Gases. — The  volume  of  gases,  owing  to  their  great 
expansibility  and  compressibility,  is  subject  to  enormous  variations. 
Hence,  in  stating  the  absolute  density  of  a  gas,  it  is  very  important 
to  specify  the  temperature  and  pressure  at  which  we  suppose  it  to  be 
taken. 

In  stating  the  specific  gravity  or  relative  density  of  a  gas  as  com- 
pared with  dry  atmospheric  air,  which  is  always  adopted  as  the  stan- 
dard substance,  it  is  to  be  understood  that  the  gas  is  at  the  same 
temperature  and  pressure  as  the  air  with  which  it  is  compared;  and, 
in  consequence  of  the  inexactness  of  the  laws  of  Boyle  and  Gay- 
Lussac,  it  is  further  necessary,  for  purposes  of  accuracy,  to  specify 
the  temperature  and  pressure  at  which  the  comparison  is  made. 
These  are  usually  the  temperature  0°  C.,  and  the  pressure  of  760  milli- 
metres. The  specific  gravity  or  relative  density  of  a  gas  is  therefore 
defined  as  the  ratio  of  the  weight  of  any  volume  of  the  gas  at  the 
temperature  0°  C.,  and  the  pressure  of  760  millimetres,  to  the  weight 
of  the  same  volume  of  dry  air  at  the  same  temperature  and  pressure. 

This  ratio  being  known,  we  can  deduce  from  it  the  weight  of  any 
volume  of  the  gas  in  question,  by  employing  as  a  factor  the  weight 


DENSITY   OF  A   GAS. 


of  unit  volume  of  air  (§  100).  Thus,  for  instance,  the  ratio  of  the 
density  of  oxygen  to  that  of  air  being  1'1056,  and  the  weight  of  a 
litre  of  air  at  0°  C.  and  7GO  millimetres  being  T293  gramme,  we 
conclude  that  the  weight  of  a  litre  of  oxygen  at  this  temperature  and 
pressure  is  1*293x1 '1056 =1*429  gramme. 

221.  Measurement  of  the  Density  of  a  Gas. — The  densities  of  gases 
have  been  the  subject  of  numerous  investigations;  we  shall  here 
mention  only  the  ingenious  and  exact  method  employed  by  Regnault. 
The  gas  is  inclosed  in  a  globe,  of  about  12  litres'  capacity,  and  fur- 
nished with  a  stop-cock.  This  communicates  with  a  three-way  tube, 
furnished  with  stop-cocks  a  and  b  (Fig.  218),  and  through  it  with  an 
air-pump  on  one  side,  and  a  manometer  on  the  other.  The  globe  is 
exhausted  several  times,  and  each  time  the  gas  is  dried  on  its  way  to 
the  globe  by  passing  through  a  number  of  tubes  containing  pieces  of 
pumice-stone  moistened  with  sulphuric  acid.  When  all  moisture  is 
supposed  to  be  removed,  the  globe  is  surrounded  with  melting  ice, 


Fig.  218.— Measurement  of  Density  of  Gases. 


Fig.  219.— Compensating  Globe. 


and  is  allowed  to  fill  with  gas  at  the  pressure  of  the  atmosphere. 
When  equilibrium  of  temperature  has  been  established,  the  globe  is 
taken  out,  carefully  dried,  and  suspended  from  one  of  the  scales  of  a 
balance.  From  the  other  scale  is  suspended  a  globe  of  the  same 
glass,  and  of  the  same  external  volume  (Fig.  219).  The  equality  of 
the  volumes  is  tested  by  weighing  each  in  water,  and  noting  the 
upward  pressure  of  the  liquid  in  each  case.  Weights  are  now  added 
until  equilibrium  is  established;  and  it  can  be  proved  that  this  equili- 
brium will  be  rigorously  maintained,  whatever  be  the  variations  of 


296  EXPANSION   OF   GASES. 

external  pressure  and  temperature,  because  these  variations  will 
produce  the  same  effect  upon  both  globes.  It  is  this  introduction  of 
a  compensating  globe  which  gives  Regnault's  method  its  great  pre- 
cision;1 for  since  all  external  causes  that  could  disturb  equilibrium 
are  balanced,  the  observed  differences  in  weight  can  result  only  from 
variations  in  the  gas  inside. 

The  globe  is  then  again  surrounded  with  ice,  communication  with 
the  air-pump  and  the  manometer  is  established,  and  a  partial  vacuum 
is  produced  as  far  as  a  certain  limit  h.  On  the  globe  being  again 
suspended  from  the  scale,  the  equilibrium  of  the  balance  is  disturbed, 
and  the  weight  w,  necessary  to  re-establish  it,  is  evidently  equal  to 
the  weight  of  a  volume  of  dry  gas  at  0°,  and  at  the  pressure  H—  h, 
H  being  the  external  pressure.  Hence  it  follows  that  the  weight  of 
dry  gas  which  would  completely  fill  the  globe  at  the  temperature  of 
0°,  and  at  the  pressure  of  760  millimetres,  is 


. 

H-A 

The  same  experiment,  when  performed  with  air,  would  give  as  the 
weight  of  the  same  volume  of  this  gas  under  the  same  conditions 

'     76° 


The  relative  density  of  the  given  gas  is  therefore 


760  ^_   ,    760 
'  W 


222.  Weight  of  a  Litre  of  Air.  —  The  preceding  experiments  give 
the  weight  of  dry  air  which  fills  a  given  globe  at  0°,  and  at  a  pressure 
of  760  millimetres.  In  order  to  know  the  weight  of  a  litre  of  air, 
we  have  only  to  observe  the  weight  of  water  which  fills  the  same 
globe  at  a  given  temperature.  Let  m  be  the  difference  of  weight  of 
the  globe  when  filled  with  water  and  with  dry  air;  then  the  weight 
of  the  water  contained  in  the  globe  is  evidently  m  plus  the  weight 
of  the  dry  air,  which  is  previously  known,  and  which  we  shall  denote 
by  a.  Let  x  be  the  volume  of  the  globe,  and  v  the  expansion  of  the 
water  from  4°  C.  to  the  temperature  of  weighing.  Then,  if  the  gramme 
and  cubic  centimetre  be  the  units  of  weight  and  volume,  we  have  the 
equation 


1  The  same  device  had  previously  been  employed  by  Dr.  Prout  in  determining  the  weight 
of  air. 


WEIGHT  OF  AIK.  297 

which  gives  the  volume  of  the  globe  at  a  known  temperature,  whence 
the  volume  at  zero  may  be  deduced. 

Various  minute  precautions  are  necessary  in  order  to  fill  the  globe 
with  water  completely  free  from  air,  and  in  order  to  insure  that  the 
temperature  shall  be  the  same  throughout  the  whole  of  the  consider- 
able volume  employed  in  the  experiment.  The  first  condition  is 
especially  difficult  to  fulfil;  in  order  to  attain  it,  Regnault  first 
expelled  the  air  from  the  globe  by  introducing  a  small  quantity  of 
water,  and  then  exhausting  the  globe,  the  process  being  aided  by  a 
slight  elevation  of  temperature;  on  the  other  hand,  water,  from  which 
the  air  had  been  expelled  by  boiling,  was  forced  by  the  pressure  of 
steam  into  a  tube  leading  to  the  stop-cock  of  the  exhausted  globe, 
so  as  to  be  nowhere  exposed  to  the  atmosphere.  The  difficulties  of 
this  process  were  skilfully  overcome  by  Regnault,  and  he  finally 
arrived  at  the  following  result. 

In  Paris,  at  a  height  of  60  metres  above  the  level  of  the  sea,  a  litre 
of  dry  air,  at  the  temperature  of  0°  C.,  .and  a  pressure  of  760  milli- 
metres, weighs  1*2932  gramme.  A  pressure  of  760  millimetres  of 
mercury  has  not  the  same  effective  value  at  different  parts  of  -the 
globe,  on  account  of  the  variations  in  the  intensity  of  gravity,  whence 
it  follows  that  the  weight  of  the  litre  of  air,  defined  by  the  preceding 
conditions,  varies  proportionally  to  the  value  of  g.  (See  note  to  §  100.) 

The  following  table  gives  the  densities  of  several  gases  at  0°  C.,  and 
under  the  pressure  of  760  millimetres  at  Paris:  — 


Air  ....................................     1  ......  1-2932 

Oxygen  ...............................     M0563        _______  T4298 

Hydrogen  ............................       '06926         ......  '08957 

Nitrogen  ..............................       '97137        ......  1-25615 

Chlorine  .............................     2'4216  ......  31328 

Carbonic  oxide  .....................       -9569          ......  T2344 

Carbonic  acid  ......................     1-52901         ......  1'9774 

Protoxide  of  nitrogen  .............     1'5269  ......  T9697 

Binoxide  of  nitrogen  ...............     1-0388  .....  T3434 

Sulphurous  acid  .....................     2'1930          .....  27289 

Cyanogen  ............................     1-8064          ......  2'3302 

Marsh-gas  ..........................  .       '559  ......  '727 

Olefiantgas  ..........................       '985  ......  1-274 

Ammonia  ............................       '59G7          ......  '7697 

^  223.  Draught  of  Chimneys.  —  The  expansion  of  air  by  heat  pro- 
duces the  upward  current  in  chimneys,  and  an  approximate  expres- 
sion for  the  velocity  of  this  current  may  be  obtained  by  the  applica- 


298 


EXPANSION   OF   GASES. 


tion  of  Torricelli's  theorem  on  the  efflux  of  fluids  from  orifices  (Chap, 
xviil). 

Suppose  the  chimney  to  be  cylindrical  and  of  height  h.  Let  the 
air  within  it  be  at  the  uniform  temperature  if  Centigrade,  and  the 
external  air  at  the  uniform  temperature  t  According  to  Torricelli's 
theorem,  the  square  of  the  linear  velocity  of  efflux  is  equal  to  the 
product  of  2g  into  the  head  of  fluid,  the  term  head  of  fluid  being 
employed  to  denote  the  pressure  producing  efflux,  expressed  in  terms 
of  depth  of  the  fluid. 

In  the  present  case  this  head  is  the  difference  between  h,  which  is 
the  height  of  air  within  the  chimney,  and  the  height  which  a  column 
of  the  external  air  of  original  height  h  would  have  if  expanded 
upwards,  by  raising  its  temperature  from  t  to  t'.  This  latter  height 

is  h 


I  +  at' 


l  +  at  )  a  denoting  the  coefficient  of  expansion  '00366;  and  the 
head  is 

_hr_ha(t'-t) 


l  +  at 


l  +  at 


Hence,  denoting  by  v  the  velocity  of  the  current  up  the  chimney,  we 
have 


l  +  at 


This  investigation,  though  it  gives  a  result  in  excess  of  the  truth, 
from  neglecting  to  take  account  of  friction  and  eddies,  is  sufficient  to 
explain  the  principal  circumstances  on  which  the  strength  of  draught 


Fig.  220.— Kumford's  Fire-place. 


depends.  It  shows  that  the  draught  increases  with  the  height  h  of 
the  chimney,  and  also  with  the  difference  t'  —  t  between  the  internal 
and  external  temperatures. 


DRAUGHT   OF   CHIMNEYS. 


299 


The  draught  is  not  so  good  when  a  fire  is  first  lighted  as  after  it 
has  been  burning  for  some  time,  because  a  cold  chimney  chills  the 
air  within  it.  On  the  other  hand,  if  the  fire  is  so  regulated  as  to 
keep  the  room  at  the  same  temperature  in  all  weathers,  the  draught 
will  be  strongest  when  the  weather  is  coldest. 

The  opening  at  the  lower  end  of  the  chimney  should  not  be  too 
wide  nor  too  high  above  the  fire,  as  the  air  from  the  room  would  then 
enter  it  in  large  quantity,  without  being  first  warmed  by  passing 
through  the  fire.  These  defects  prevailed  to  a  great  extent  in  old 
chimneys.  Rumford  was  the  first  to  attempt  rational  improvements. 
He  reduced  the  opening  of  the  chimney  and  the  depth  of  the  fire- 
place, and  added  polished 
plates  inclined  at  an  angle, 
which  serve  both  to  guide 
the  air  to  the  fire  arid  to  re- 
flect heat  into  the  room  (Fig. 
220). 

The  blower  (Fig.  221)  pro- 
duces its  well-known  effects 
by  compelling  all  air  to  pass 
through  the  fire  before  enter- 
ing the  chimney.  This  at 
once  improves  the  draught  of 
the  chimney  by  raising  the 

temperature  of  the  air  within  it,  and  quickens  combustion  by  in- 
creasing the  supply  of  oxygen  to  the  fuel. 

224.  Stoves. — The  heating  of  rooms  by  open  fire-places  is  effected 
almost  entirely  by  radiation,  and  much  even  of  the  radiant  heat  is 
wasted.  This  mode  of  heating  then,  though  agreeable  and  healthful, 
is  far  from  economical.  Stoves  have  a  great  advantage  in  point  of 
economy,  for  the  heat  absorbed  by  their  sides  is  in  great  measure 
given  out  to  the  room,  whereas  in  an  ordinary  fire-place  the  greater 
part  of  this  heat  is  lost.  Open  fire-places  have,  however,  the  advan- 
tage as  regards  ventilation;  the  large  opening  at  the  foot  of  the 
chimney,  to  which  the  air  of  the  room  has  free  access,  causes  a  large 
body  of  air  from  the  room  to  ascend  the  chimney,  its  place  being 
supplied  by  fresh  air  entering  through  the  chinks  of  the  doors  and 
windows,  or  any  other  openings  which  may  exist. 

Stoves  are  also  liable  to  the  objection  of  making  the  air  of  the  room 
too  dry,  not,  of  course,  by  removing  water,  but  by  raising  the  tem- 


Fig.  221.— Fire-place  with  Blower. 


300 


EXPANSION  OF   GASES. 


perature  of  the  air  too  much  above  the  dew-point  (Chap,  xxviii.).  The 
same  thing  occurs  with  open  fire-places  in  frosty  weather,  at  which 
time  the  dew-point  is  unusually  low.  This  evil  can  be  remedied  by 
placing  a  vessel  of  water  on  the  stove.  The  reason  why  it  is  more 
liable  to  occur  with  stoves  than  with  open  fire-places,  is  mainly  that 
the  former  raise  the  air  in  the  room  to  a  higher  temperature  than 
the  latter,  the  defect  of  air-temperature  being  in  the  latter  case  com- 
pensated by  the  intensity  of  the  direct  radiation  from  the  glowing 
fuel. 

Fire-clay,  from  its  low  conducting  power,  is  very  serviceable  both 
for  the  backs  of  fire-places  and  for  the  lining  of  stoves.     In  the  former 

situation  it  prevents  the  wasteful 
escape  of  heat  backwards  into  the 
chimney,  and  keeps  the  back  of  the 
fire  nearly  as  hot  as  the  centre.  As 
a  lining  to  stoves,  it  impedes  the 
lateral  escape  of  heat,  thus  answer- 
ing the  double  purpose  of  prevent- 
ing the  sides  of  the  stove  from  over- 
heating, and  at  the  same  time  of 
keeping  up  the  temperature  of  the 
fire,  and  thereby  promoting  com- 
plete combustion.  Its  use  must, 
however,  be  confined  to  that  por- 
tion of  the  stove  which  serves  as 
the  fire-box,  as  it  would  otherwise 
prevent  the  heat  from  being  given 
out  to  the  apartment. 

The  stove  represented  in  Fig.  2221 
belongs  to  the  class  of  what  are 
called  in  France  calori/eres,  and  in 
England  ventilating  stoves,  being 
constructed  with  a  view  to  promot- 
ing the  circulation  and  renewal  of 
the  air  of  the  apartment.  G  is  the  fire-box,  over  which  is  the  feeder 
U,  containing  uriburned  fuel,  and  tightly  closed  at  top  by  a  lid,  which 
is  removed  only  when  fresh  fuel  is  to  be  introduced.  The  ash-pan 
F  has  a  door  pierced  with  holes  for  admitting  air  to  support  com- 

1  With  the  exception  of  the  ventilating  arrangement,  this  stove  is  identical  with  what  is 
known  in  this  country  as  Walker's  self- feeding  stove. 


Fig.  222.— Ventilating  Stove. 


VENTILATING   STOVE.  301 

bustion.  The  flame  and  smoke  issue  at  the  edge  of  the  fire-box,  and 
after  circulating  round  the  chamber  O  which  surrounds  the  feeder, 
enter  the  pipe  T  which  leads  to  the  chimney.  The  chamber  0  is 
surrounded  by  another  iiiclosure  L,  through  which  fresh  air  passes, 
entering  below  at  A,  and  escaping  into  the  room  through  perforations 
in  the  upper  part  of  the  stove  as  indicated  by  the  arrows.  The 
amount  of  fresh  air  thus  admitted  can  be  regulated  by  the  throttle- 
valve  P. 


CHAPTER    XXIV. 


FUSION    AND    SOLIDIFICATION. 


225.  Fusion.  —  -Many  spljd  bodies,  \\hen  raised  to  a  sufficiently  high 
id 


tem;pe7'iti£r£0m£  liqui  This  change  of  state  is  called  melting 
or  fusion,  and  the  temperature  at  which  it  occurs  (called  the  melting- 
point,  or  temperature  of  fusion)  is  constant  for  each  substance,  with 
the  exception  of  the  variations  —  which  in  ordinary  circumstances  are 
insignificant  —  due  to  differences  of  pressure  (§  237).  The  melting- 
points  of  several  substances  are  given  in  the  following  table:  — 

TABLE  OF  MELTING-POINTS,  IN  DECREES  CENTIGRADE. 


Mercury, -39 

.Ice, 0 

Butter, 33 

Lard, 33 

Spermaceti, 49 

Stearine, 55 

Yellow  Wax, 62 

White  Wax, 68 

Stearic  Acid, 70 

Phosphorus, 44 

Potassium, 63 

Sodium, ....  95 

Iodine, 107 

Sulphur, 110 


Tin, 230 

Bismuth, 562 

Lead,        320 

Zinc, 360 

Antimony, 432 

Bronze, 900 

Pure  Silver, 1000 

Copper, lloO 

Coined  Gold, 1180 

Pure  Gold, 1250 

Cast  Iron,          1050  to  1250 

Steel,        1300  to  1400 

Wrought  Iron,        ....     1500  to  1600 
Platinum,  .  2000 


Some  bodies,  such  as  charcoal,  have  hitherto  resisted  all  attempts 
to  reduce  them  to  the  liquid  state;  but  this  is  to  be  attributed  only 
to  the  insufficiency  of  the  means  which  we  are  able  to  employ. 

It  is  probable  that,  by  proper  variations  of  temperature  and  pres- 
sure, all  simple  substances,  and  all  compound  substances  which  would 
not  be  decomposed,  could  be  compelled  to  assume  the  three  forms, 
solid,  liquid,  and  gaseous. 

The  passage  from  the  solid  to  the  liquid  state  is  generally  abrupt; 


LATENT   HEAT   OF   FUSION. 


303 


but  this  is  not  always  the  case.     Glass,  for  instance,  before  reaching 
a  state  of  perfect  liquefaction,  passes  through  a  series  of  intermediate 
stages  in  which  it  is  of  a  viscous  consistency,  and  can  be  easily  drawn 
out  into  exceedingly  fine  threads,  or  moulded  into  different  shapes. 
/  226.  Constant  Temperature  during  Fusion. — During  the  entire  time 
of  fusion  the  temperature  remains  constant.     Thus  if  a  vessel  con- 
taining ice  be  placed  on  the  fire,  the  ice  will  melt  more  quickly  as 
the  fire  is  hotter;  but  if  the  mixture  of  ice  and  water  be  constantly 
stirred,  a  thermometer  placed  in  it  will  indicate  the  temperature 
zero  without  variation  so  long  as  any  ice  re- 
mains unmelted;    it  is  only  after  all  the  ice 
has  become  liquid  that  a  rise  of  temperature 
will  be  observed. 

In  the  same  way,  if  sulphur  be  heated  in  a 
glass  vessel,  the  temperature  indicated  by  a 
thermometer  placed  in  the  vessel  will  rise  grad- 
ually until  it  reaches  about  110°,  when  a  por- 
tion of  the  sulphur  will  be  seen  to  become 
liquid,  and  if  the  vessel  be  shaken  during  the 
time  of  fusion,  until  the  whole  of  the  sulphur 
is  liquefied,  the  temperature  will  be  observed 
to  remain  steadily  at  this  point, 
fv  227.  Latent  Heat  of  Fusion.  —  This  con- 
stancy of  temperature  is  very  remarkable, 

and  leads  to  some  important  conclusions.  In  fact,  as  the  action 
of  the  fire  continues  the  same  throughout  the  entire  time  of  fusion, 
while  the  thermometer  remains  stationary,  all  the  heat  supplied 
after  liquefaction  has  begun,  appears  to  be  lost.  Hence  we  con- 
clude, that  in  order  that  a  body  may  pass  from  the  solid  to  the 
liquid  state,  it  must  absorb  a  certain  quantity  of  heat  which  produces 
no  thermometric  effect.  Black,  who  was  the  first  to  investigate  this 
subject,  gave  to  the  heat  thus  absorbed  the  name  of  latent  heat,  by 
which,  it  is  still  usually  designated.  A  similar  absorption  of  heat 
without  thermometric  effect  occurs  when  a  boiling  liquid  is  converted 
into  vapour.  Hence  it  is  necessary  to  distinguish  between  the  lateitt 
heat  of  fusion  and  the  latent  heat  of  vaporization.1  Latent  heat 
then  may  be  defined  as  the  heat  absorbed  in  virtue  of  change  of 

1  The  former  is  often  called  the  latent  heat  of  the  liquid,  and  the  latter  of  the  vapour. 
Thus  we  speak  of  the  latent  heat  of  water  (which  becomes  latent  in  the  melting  of  ice), 
and  of  the  latent  heat  of  steam  (which  becomes  latent  in  the  vaporization  of  water). 


Fig.  223. — Fusion  of  Sulphur. 


304  FUSION  AND   SOLIDIFICATION. 

state  from  solid  to  liquid,  or  from  liquid  to  gaseous.  Modern  philo- 
sophy teaches  that  the  processes  of  fusion  and  vaporization  involve 
the  performance  of  work  by  heat  in  opposition  to  molecular  force,  and 
that  an  amount  of  heat  disappears  (or  becomes  latent)  which  is  the 
exact  equivalent  of  the  work  performed. 

\  228.  Heat  of  Fusion  of  Ice.— The  latent  heat  of  fusion  is  different 
for  different  substances.  Its  amount  for  ice  (commonly  called  the 
latent  heat  of  water)  can  be  approximately  determined  by  the  follow- 
ing experiment,  which  is  due  to  Black,  who  was  the  first  to  make 
accurate  observations  on  this  subject. 

Take  a  pound  of  ice  at  0°  C.  and  a  pound  of  water  at  79°  C.  ;  let 
the  water  be  poured  over  the  ice,  and  the  mixture  rapidly  stirred. 
The  ice  will  melt,  and  two  pounds  of  water  at  0°  will  be  obtained. 
This  interesting  experiment  shows  that  all  the  heat  necessary  to  raise 
a  pound  of  water  from  0°  to  79°  has  been  absorbed  in  melting  a  pound 
of  ice;  and  it  is  thus  directly  proved  that  the  heat  required  to  melt  a 
pound  of  ice  is  exactly  the  same  as  that  required  to  raise  the  tem- 
perature of  a  pound  of  water  from  0°  to  79°. 

The  name  unit  of  heat  is  given  to  the  amount  of  heat  necessary 
to  raise  unit  mass  of  water  one  degree  It  will  be  different  according 
to  the  unit  of  mass  and  scale  of  temperature  adopted.  The  pound- 
centigrade  unit  is  the  heat  required  to  raise  a  pound  of  water  through 
one  degree  Centigrade,  and  we  see  from  above  that  79  of  these  units 
are  required  for  the  melting  of  a  pound  of  ice.1 

On  comparing  the  heat  of  fusion  of  ice  with  that  of  some  other 
bodies  as  given  in  the  table  §  348,  it  will  be  seen  that  its  amount  is 
notably  greater  for  ice  than  for  any  of  the  other  substances.  Ice  is 
in  this  sense  the  most  difficult  to  melt,  and  water  tlfe  most  difficult 
to  freeze  of  all  substances,  a  fact  which  is  of  immense  importance  in 
the  economy  of  nature,  as  tending  to  retard  the  processes  both  of 
freezing  and  thawing.  Even  as  it  is,  the  effects  of  a  sudden  thaw  are 
often  very  disastrous,  and  yet,  for  every  pound  of  ice  melted,  as  much 
heat  is  required  as  would  raise  the  water  produced  through  79°  C. 
or  142°  F. 

--  229.  Solution. — The  reduction  of  a  body  from  the  solid  to  the  liquid 
state  may  be  effected  by  other  means  than  by  the  direct  action  of 
heat ;  it  may  be  produced  by  the  action  of  a  liquid.  This  is  what 
occurs  when,  for  instance,  a  grain  of  salt  or  of  sugar  is  placed  in 

1  The  statements  in  this  paragraph,  including  the  definition  of  a  unit  of  heat,  are  only 
approximate.     The  subject  will  be  resumed  in  Chap.  xxxi. 


FREEZING  MIXTURES. 


305 


water;  the  body  is  said  to  melt  or  dissolve  in  the  water.  Solution, 
like  fusion,  is  accompanied  by  the  disappearance  of  heat  consequent 
on  the  change  from  the  solid  to  the  liquid  state.  For  example,  when 
nitrate  of  ammonia  is  rapidly  dissolved  in  water,  a  fall  of  from  20° 
to  25°  Cent,  is  observed. 

Unlike  fusion,  it  is  attached  to  no  definite  temperature,  but  occurs 
with  more  or  less  freedom  over  a  wide  range.  Rise  of  temperature 
usually  favours  it;  but  there  are  some  strongly  marked  exceptions. 
7^230.  Freezing  Mixtures. — The  absorption  of  heat  which  accom- 
panies the  liquefaction  of  solids  is  the  basis  of  the  action  of  freezing 
mixtures.  In  all  such  mixtures  there  is  at  least  one  solid  ingredient 
which,  by  the  action  of  the  rest,  is  reduced  to  the  liquid  state,  thus 
occasioning  a  fall  of  temperature  proportional  to  the  latent  heat  of 
its  liquefaction. 

The  mixture  most  commonly  employed  in  the  laboratory  is  one  of 
snow  and  salt,  in  the  proportion  of  two  parts  of  the  former  to  one  of 
the  latter.  This  mixture  assumes  a  temperature  of  about  —18°  C.  (0°F.), 
and  furnished  Fahrenheit  with  the  zero  of  his  scale.  In  this  instance 
there  is  a  double  absorption  of  heat  caused  by  the  simultaneous  melt- 
ing of  the  snow  and  dissolving  of  the  salt. 

We  may  obtain  a  freezing  mixture  without  the  use  of  snow  or  ice. 
Such  mixtures  are  often  employed  for  the  artificial  freezing  of  water. 
Various  kinds  of  apparatus  have  been  invented  for  this  purpose,  one 
of  which  is  shown  in  Fig.  224.  It  consists  of  a  metal  cylinder,  con- 


Fig.  224.— Freezing  Rocker. 


taining  the  freezing  mixture  (hydrochloric  acid  and  sulphate  of  soda). 
In  the  cylinder  is  placed  a  mould  formed  of  two  concentric  vessels 
with  the  water  between  them,  an  arrangement  which  has  the  advan- 
tage of  increasing  the  surface  of  contact.  The  whole  is  set  upon  a 
cradle,  the  rocking  of  which  greatly  assists  the  operation.  We  sub- 


20 


306  FUSION   AND  SOLIDIFICATION. 

join  a  table  of  the  most  important  freezing  mixtures,  with  the  pro- 
portions corresponding  to  the  maximum  effect.  These  proportions 
are  evidently  of  importance,  since  the  amount  of  heat  absorbed  in  a 
given  time  depends  upon  the  quantity  of  solid  matter  that  is  reduced 
to  the  liquid  state  during  that  time.  There  may  also  be  chemical 
action  between  the  materials  of  which  the  mixture  is  composed.  This 
is  always  attended  with  generation  of  heat,  so  that  in  this  case  the 
actual  result  depends  upon  the  difference  of  two  opposite  effects. 
Thus  the  mixture  of  four  parts  of  sulphuric  acid  with  one  of  ice 
causes  a  rise  of  temperature  of  about  50°  or  60°,  while  four  parts  of 
ice  and  one  of  sulphuric  acid  produce  a  cold  of  from  —15°  to  —20°  C. 

TABLE. 

Proportions         Fall  of  Temperature 
by  Weight.        in  Centigrade  degrees. 

Snow  or  Powdered  Ice,    ......       2J      from0°to-2r. 

Bay-salt,  ...........       1  J 

Snow»  ............       H     fromO°to-4S°. 

Crystallized  Chloride  of  Calcium,    ...       4  ) 

Nitrate  of  Ammonia,  .......  1)      from  +1(r  to  -15°. 

Water,       ...........  1  ) 

Sal-ammoniac,     .......     .     .  5 

Nitrate  of  Potash,         .......  5 

Sulphate  of  Soda,     ........  8 

Water,        ...........  16 

Sulphate  of  Soda,    ........  8|      frorn  +  10o  to  -  17°. 

Hydrochloric  Acid,       .......  5  ) 


from  +10°  to  -15°. 


1.  Solidification  or  Congelation.  —  Congelation  is  the  inverse  of 
fusion;  that  is  to  say,  it  is  the  passage  of  a  substance  from  the  liquid 
to  the  solid  state.  The  faculty  of  undergoing  this  transformation 
may  be  regarded  as  common  to  all  liquids,  although  some,  for  example, 
alcohol  and  bisulphide  of  carbon,  have  never  yet  been  solidified. 

The  temperature  of  fusion  is  the  highest  temperature  at  which 
congelation  can  occur,  and  is  frequently  called  the  temperature  of 
congelation  (or  the  freezing  -point]  ;  but  it  is  possible  to  preserve 
substances  in  the  liquid  state  at  lower  temperatures.  Liquids  thus 
cooled  below  their  so-called  freezing-points  have,  however,  if  we  may 
so  say,  a  tendency  to  freeze,  which  is  only  kept  in  check  ~by  the  diffi- 
culty of  making  a  commencement.  If  freezing  once  begins,  or  if 
ever  so  small  a  piece  of  the  same  substance  in  the  frozen  state  be 
allowed  to  come  in  contact  with  the  liquid,  congelation  will  quickly 
extend  until  there  is  none  of  the  liquid  left  at  a  temperature  below 
that  of  fusion.  The  condition  of  a  liquid  cooled  below  its  freezing- 


CRYSTALLIZATION.  307 

point  has  been  aptly  compared  to  that  of  a  row  of  bricks  set  on  end 
in  such  a  manner  that  if  the  first  be  overturned,  it  will  cause  all  the 
rest  to  fall,  each  one  overturning  its  successor. 

The  contact  of  its  own  solid  infallibly  produces  congelation  in  a 
liquid  in  this  condition,  and  the  same  effect  may  often  be  produced 
by  the  contact  of  some  other  solid,  especially  of  a  crystal,  or  by  giving 
a  slight  jar  to  the  containing  vessel. 

Despretz  has  cooled  water  to  —  20°  C.  in  fine  capillary  tubes,  with- 
out freezing,  and  Dufour  has  obtained  a  similar  result  by  suspending 
globules  of  water  in  a  liquid  of  the  same  specific  gravity  with  which 
it  would  not  mix. 

/  232.  Heat  set  free  in  Congelation. — At  the  moment  when  congela- 
tion takes  place,  the  thermometer  immediately  rises  to  the  tempera- 
ture of  the  melting-point.  This  may  be  easily  shown  by  experiment 
A  small  glass  vessel  is  taken,  containing  water,  in  which  a  mercurial 
thermometer  is  plunged.  By  means  of  a  frigorific  mixture  the  tem- 
perature is  easily  lowered  to  —  1 0°  or  —  1 2°,  without  the  water  freez- 
ing; a  slight  shock  is  then  given  to  the  glass,  congelation  takes  place, 
and  the  mercury  rises  to  0°. 

The  heat  thus  produced  is  the  equivalent  of  the  work  done  by  the 
molecular  forces  of  the  body  in  the  passage  from  the  liquid  to  the 
solid  state.  The  quantity  of  heat  thus  arising  is  evidently  the  same 
as  that  which  disappears  in  fusion,  since  they  are  the  equivalents  of 
the  same  amount  of  work  performed  in  opposite  directions.  The 
production  of  this  heat  may  be  experimentally  shown  in  another  way. 
If  we  heat  a  quantity  of  lead  to  its  melting-point  (320°),  and  when 
the  metal  is  just  beginning  to  melt,  plunge  it  into  water,  a  certain 
rise  of  temperature  will  be  observed.  If  we  repeat  the  same  experi- 
ment, allowing  the  lead  time  to  melt  completely,  the  temperature 
being  still  320°,  a  much  more  considerable  increase  in  the  temperature 
of  the  water  will  be  produced,  the  reason  being  that  the  lead  in 
solidifying  in  contact  with  the  water  gives  out  its  latent  heat. 
T"  233.  Crystallization. — When  the  passage  from  the  liquid  to  the 
solid  state  is  a  gradual  one,  it  frequently,  happens  that  the  molecules 
group  themselves  in  such  a  manner  as  to  present  regular  geometric 
forms.  This  process  is  called  crystallization,  and  the  regular  bodies 
thus  formed  are  called  crystals.  The  particular  crystalline  form 
assumed  depends  upon  the  substance,  and  often  affords  a  means  of 
recognizing  it.  The  forms,  therefore,  in  which  bodies  crystallize 
are  among  their  most  important  characteristics,  and  are  to  some 


308  FUSION   AND   SOLIDIFICATION. 

extent  analogous  to  the  shapes  of  animals  and  plants  in  the  organic 
world. 

In  order  to  make  a  body  crystallize  in  solidifying,  the  following 
method  is  employed.  Suppose  the  given  body  to  be  bismuth  ;  the 
first  step  is  to  melt  it,  and  then  leave  it  to  itself  for  a  time.  The 
metal  naturally  begins  to  solidify  first  at  the  surface  and  at  the  sides, 
where  it  is  most  directly  exposed  to  cooling  influences  from  without ; 
accordingly,  when  the  outer  layer  of  the  metal  is  solidified,  the  in- 
terior is  still  in  the  liquid  state.  If  the  upper  crust  be  now  removed, 
and  the  liquid  bismuth  poured  off,  the  sides  of  the  vessel  will  be  seen 
to  be  covered  with  a  number  of  beautiful  crystals. 

If  the  metal  were  allowed  to  stand  too  long,  the  entire  mass  would 
become  solid,  the  different  crystals  would  unite,  and  no  regularity  of 
structure  would  be  observable.  This  is  the  case  with  a  great  number 
of  solids ;  ice  is  one  very  remarkable  instance. 

s-  234.  Flowers  of  Ice. — The  tendency  of  ice  to  assume  a  crystalline 
form  is  seen  in  the  fern-leaf  patterns  which  appear  on  the  windows 
in  winter,  caused  by  the  congealing  of  moisture  on  them,  and  still 
more  distinctly  in  the  symmetrical  forms  of  snow-flakes  (see  Chap, 
xxviii.)  In  a  block  of  ice,  however,  this  crystalline  structure  does 
not  show  itself,  owing  to  the  closeness  with  which  the  crystals  fit  into 
each  other,  so  that  a  mass  of  this  substance  appears  almost  completely 
amorphous.  Tyndall,  however,  in  a  very  interesting  experiment, 
has  succeeded  in  gradually  decry stallizing  ice,  if  we  may  use  the 


Fig.  225. — Flowers  of  Ice  projected  on  a  Screen. 

expression,  and  thus  exhibiting  the  crystalline  elements  of  which  it 
is  composed.  The  experiment  consists  in  causing  a  pencil  of  solar 
rays  to  fall  perpendicular  to  the  surfaces  of  congelation  on  a  sheet  of 
ice,  such  as  is  naturally  formed  upon  the  surface  of  water  in  winter. 
A  lens  placed  behind  the  ice  (Fig.  225)  serves  to  project  upon  a  screen 


FLOWERS  OF   ICE. 


309 


the  linage  of  what  is  found  in  the  interior  of  the  block.     The  succes- 

O 

sive  appearances  observed  upon  the  screen  are  shown  in  Fig.  226. 
A  small  luminous  circle  is  first  seen,  from  which  branch  out  rays, 
resembling  the  petals  of  a  flower  whose  pistil  is  the  circle.  Frequent 
changes  also  occur 
in  the  shape  of 
the  branches  them- 
selves, which  are 
often  cut  so  as 
to  resemble  fern- 
leaves,  like  those 
seen  upon  the  win- 
dows during  frost. 
In  this  experiment 
the  solar  heat,  in- 
stead of  uniformly 
melting  the  mass 
of  ice,  which  it 
would  certainly  do 
if  the  mass  were 
amorphous,  acts 
successively  upon 
the  different  crys- 
tals of  which  it  is 
built  up,  affecting 
them  in  the  re- 
verse order  of  their 
formation.  There 
are  thus  produced 
a  number  of  spaces 
of  regular  shape, 
containing  water, 
and  producing 
comparatively 
dark  images  upon 

the  screen.  In  the  centre  of  each  there  is  generally  a  bright  spot, 
which  corresponds  to  an  empty  space,  depending  on  the  fact  that 
the  water  occupies  a  smaller  volume  than  the  ice  from  which  it  has 
been  produced. 

235.  Supersaturation, — The  proportion  of  solid  matter  which  a  liquid 


Fig.  226.— Flowers  of  Ice. 


310 


FUSION   AND   SOLIDIFICATION. 


can  hold  in  solution  varies  according  to  the  temperature ;  as  a  general 
rule,  though  not  by  any  means  in  all  cases,  it  increases  as  the  tem- 
perature rises.  Hence  it  follows,  that  if  a  saturated  solution  be  left 
to  itself,  the  effect  of  evaporation  or  cooling  will  be  gradually  to  dim- 
inish the  quantity  of  matter  which  can  be  held  in  solution.  A  portion 
of  the  dissolved  substance  will  accordingly  pass  into  the  solid  state, 
assuming .  generally  a  crystalline  form.  This  is  an  exceedingly  com- 
mon method  of  obtaining  crystals,  and  is  known  as  the  humid  way. 
In  connection  with  this  process  a  phenomenon  occurs  which  is 
precisely  analogous  to  the  cooling  of  a  liquid  below  its  freezing-point. 
It  may  be  exemplified  by  the  following  experiment. 

A  tube  drawn  out  at  one  end  (Fig.  227)  is  filled  with  a  warm  con- 
centrated solution  of  sulphate  of  soda.  The  solution  is  boiled,  and 

r\  while     ebullition     is 

proceeding  freely,  the 
tube  is  hermetically 
sealed;  by  this  means 
the  tube  is  exhausted 
of  air.  The  solution 
when  left  to  itself 
cools  without  the  sol- 
id being  precipitated, 
although  the  liquid  is 
supersaturated.  But 
if  the  end  of  the  tube 
be  broken  off,  and  the 
air  allowed  to  enter, 
crystallization  imme- 
diately commences  at 
the  surface,  and  is 
quickly  propagated 
through  the  whole 
length  of  the  tube; 
at  the  same  time,  as  we  should  expect,  a  considerable  rise  of  tem- 
perature is  observed.  If  the  phenomenon  does  not  at  once  occur 
on  the  admission  of  the  air,  it  can  be  produced  with  certainty  by 
throwing  a  small  piece  of  the  solid  sulphate  into  the  solution. 

236.  Change  of  Volume  at  the  Moment  of  Congelation.  Expansive 
Force  of  Ice. — In  passing  from  the  liquid  to  the  solid  state,  bodies 
generally  undergo  a  diminution  of  volume ;  there  are,  however, 


Fig.  227. — Preparation  of  Supersaturated  Solution  of 
Sulphate  of  Soda. 


EXPANSIVE   FORCE   OF   ICE. 


311 


exceptions,  such  as  ice,  bismuth,  silver,  and  cast-iron.  It  is  this  pro- 
perty which  renders  this  latter  substance  so  well  adapted  for  the 
purposes  of  moulding,  as  it  enables  the  metal  to  penetrate  completely 
into  every  part  of  the  mould.  The  expansion  of  ice  is  considerable, 
amounting  to  about  T*r;  its  production  is  attended  by  enormous 
mechanical  force,  just  as  in  the  analogous  case  of  expansion  by  heat. 
Its  effect  in  bursting  water-pipes  is  well  known.  The  following 
experiment  illustrates  this  expansive  force.  A  tube  of  forged  iron 
(Fig.  228)  is  filled  with  water,  and  tightly  closed  by  a  screw-stopper. 


Fig.  228.— Bursting  of  Iron  Tube  by  Expansion  of  Water  in  Freezing. 

The  tube  is  then  surrounded  with  a  freezing  mixture  of  snow  and 
salt.  After  some  time  the  water  congeals,  a  loud  report  is  often 
heard,  and  the  tube  is  found  to  be  rent. 

The  following  experiment,  performed  by  Major  Williams  at  Quebec, 
is  still  more  striking.     He  filled  a  1 2-inch  shell  with  water  and  closed 


Fig.  229.— Experiment  of  Major  Williams. 

it  with  a  wooden  stopper,  driven  in  with  a  mallet.  The  shell  was 
then  exposed  to  the  air,  the  temperature  being  —28°  C.  (—18°  F.) 
The  water  froze,  and  the  bung  was  projected  to  a  distance  of  more 
than  100  yards,  while  a  cylinder  of  ice  of  about  8  inches  in  length 
was  protruded  from  the  hole.  In  another  experiment  the  shell  split 
in  halves,  and  a  sheet  of  ice  issued  from  the  rent  (Fig.  229). 

It  is  the  expansion  and  consequent  lightness  of  ice  which  enables 


312  FUSION    AND   SOLIDIFICATION. 

it  to  float  upon  the  surface  of  water,  and  thus  afford  a  protection  to 
animal  life  below. 

237.  Effect  of  Pressure  on  the  Melting-point. — Professor  James 
Thomson  was  led  by  theoretical  considerations  to  the  conclusion  that, 
in  the  case  of  a  substance  which,  like  water,  expands  in  solidifying, 
the  freezing  (or  melting)  point  must  of  necessity  be  lowered  by  pres- 
sure, and  that  a  mixture  of  ice  and  ice-cold  water  would  fall  in 
temperature  on  the  application  of  pressure.  His  reasoning1  consisted 
in  showing  that  it  would  otherwise  be  possible  (theoretically  at  least) 
to  construct  a  machine  which  should  be  a  perpetual  source  of  work 
without  supply;  that  is,  what  is  commonly  called  a  perpetual  motion. 
The  matter  was  shortly  afterwards  put  to  the  test  of  experiment 
by  Professor  (now  Sir)  W.  Thomson,  who  compressed,  in  an  QErsted's 
piezometer,  a  mixture  of  ice  and  water,  in  which  was  inserted  a  very 
delicate  thermometer  protected  from  pressure  in  the  same  manner 
as  the  instrument  represented  in  Fig.  194c  (§189).  The  thermometer 
showed  a  regular  fall  of  temperature  as  pressure  was  applied,  followed 
by  a  return  to  0°  0.  on  removing  the  pressure.  Pressures  of  8*1  and 
16'8  atmospheres  (in  excess  of  atmospheric  pressure)  lowered  the 
freezing-point  by  '106  and  '232  of  a  degree  Fahr.  respectively  as  in- 
dicated by  the  thermometer,  results  which  agree  almost  exactly  with 
Prof.  J.  Thomson's  prediction  of  '0075  of  a  degree  Cent.,  or  '0135  of 
a  degree  Fahr.  per  atmosphere. 

Mousson  has  since  succeeded  in  reducing  the  melting-point  several 
degrees  by  means  of  enormous  pressure.  He  employed  two  forms  of 
apparatus,  by  the  first  of  which  he  melted  ice  at  the  temperature 
of  —5°  C.,  and  kept  the  water  thus  produced  for  a 
considerable  time  at  this  temperature.  This  apparatus 
had  windows  (consisting  of  blocks  of  glass)  in  its  sides, 
through  which  the  melting  of  the  ice  was  seen.  His 
second  form  of  apparatus,  which  bore  a  general  resem- 
blance to  the  first,  is  represented  in  the  annexed  figure. 
It  consisted  of  a  steel  prism  with  a  cylindrical  bore, 
Fig~23o  having  one  of  its  extremities  closed  by  a  conical 

Mousson's         stopper  strongly  screwed  in,  the  rest  of  the  bore  being 
traversed  by  a  screw-piston  of  steel.     The  apparatus 
was  inverted,  and  nearly  filled  with  water  recently  boiled,  into  which 
a  piece  of  copper  was  dropped,  to  serve  as  an  index.     The  apparatus, 

1  Transactions   Royal  Society,  Edinburgh.      January,   1849. — Cambridge  and  Dublin 
Math.  Journal.     November,  1850. 


EFFECT  OF   STKESS.  313 

still  remaining  in  the  inverted  position,  was  surrounded  by  a  freezing 
mixture,  by  means  of  which  the  water  was  reduced  to  ice  at  the  tem- 
perature of  —18°  C.  The  stopper  was  then  screwed  into  its  place, 
arid  the  apparatus  placed  in  the  erect  position.  The  piston  was  then 
screwed  clown  upon  the  ice  with  great  force,  the  pressure  exerted 
being  estimated  in  some  of  the  experiments  at  several  thousand 
atmospheres.  The  pressure  was  then  relaxed,  and,  on  removing  the 
stopper,  the  copper  index  was  found  to  have  fallen  to  the  bottom  of 
the  bore,  showing  that  the  ice  had  been  liquefied. 

Experiments  conducted  by  Bunsen  and  Hopkins  have  shown  that 
wax,  spermaceti,  sulphur,  stearin,  and  paraffin — substances  which, 
unlike  ice,  expand  in  melting — have  their  melting  points  raised  by 
pressure,  a  result  which  had  been  predicted  by  Professor  W. 
Thomson. 

237  A.  Effect  of  Stress  in  general  upon  Melting  and  Solution. — 
In  the  experiments  above  described,  the  pressure  applied  was  hydro- 
statical,  and  was  therefore  equal  in  all  directions.  But  a  solid  may  be 
exposed  to  pressure  in  one  direction  only,  or  to  pull  in  one  or  more 
directions,  or  it  may  be  subjected  to  shearing,  twisting,  or  bending 
forces,  all  these  being  included  under  the  general  name  of  stress. 

Reasoning,  based  on  the  general  laws  of  energy,  leads  to  the  con- 
clusion that  stress  of  any  kind  other  than  hydrostatic,  applied  to  a 
solid,  must  lower  its  melting-point.  To  quote  Professor  J.  Thomson 
(Vroc.Roy.Soc.  Dec.  1861),  "Any  stresses  whatever,  tending  to  change 
the  form  of  a  piece  of  ice  in  ice-cold  water,  must  impart  to  the  ice  a 
tendency  to  melt  away,  and  to  give  out  its  cold,  which  will  tend  to 
generate,  from  the  surrounding  water,  an  equivalent  quantity  of  ice 
free  from  the  applied  stresses/'  and  "stresses  tending  to  change  the 
form  of  any  crystals  in  the  saturated  solutions  from  which  they  have 
been  crystallized  must  give  them  a  tendency  to  dissolve  away,  and  to 
generate,  in  substitution  for  themselves,  other  crystals  free  from  the 
applied  stresses  or  any  equivalent  stresses."1  This  conclusion  he  ver- 
ified by  experiments  on  crystals  of  common  salt.  He  at  the  same 
time  suggested,  as  an  important  subject  for  investigation,  the  effect 

1  Professor  Thomson  draws  these  inferences  from  the  following  principle,  which  he 
assumes  (we  think  justly)  as  a  physical  axiom : — If  any  substance  or  system  of  substances 
be  in  a  condition  in  which  it  is  free  to  change  its  state  [as  ice,  for  example,  in  contact 
with  water  at  0°  C.,  is  free  to  melt],  and  if  mechanical  work  be  applied  to  it  as  potential 
energy  in  such  a  way  that  the  occurrence  of  the  change  of  state  will  make  it  lose  that 
mechanical  work  from  the  condition  of  potential  energy,  without  receiving  other  potential 
energy  as  an  equivalent;  then  the  substance  or  system  will  pass  into  the  changed  state. 


314  FUSION   AND   SOLIDIFICATI6N. 

of  hydrostatic  pressure  on  the  crystallization  of  solutions,  a  subject 
which  was  afterwards  taken  up  experimentally  by  Sorby,  who 
obtained  effects  analogous  to  those  above  indicated  as  occurring  in 
connection  with  the  melting  of  ice  and  wax. 

238.  Regulation  of  Ice. — Faraday  in  1850  called  attention  to  the 
fact  that  pieces  of  moist  ice  placed  in  contact  with  one  another  will 
freeze  together  even  in  a  warm  atmosphere.     This  phenomenon,  to 
which  Tyndall  has  given  the  name  of  regelalion,  admits  of  ready  ex- 
planation by  the  principles  just  enunciated.      Capillary  action  at  the 
boundaries  of  the  film  of  water  which  connects  the  pieces  placed  in  con- 
tact, produces  an  effect  equivalent  to  attraction  between  them,  just  as 
two  plates  of  clean  glass  with  a  film  of  water  between  them  seem  to 
adhere.     Ice  being  wetted  by  water,  the  boundary  of  the  connecting 
film  is  concave,  and  this  concavity  implies  a  diminution  of  pressure 
in  the  interior.     The  film,  therefore,  exerts  upon  the  ice  a  pressure 
less  than  atmospheric;  and  as  the  remote  sides  of  the  blocks  are  ex- 
posed to  atmospheric  pressure,  there  is  a  resultant  force  urging  them 
together  and  producing  stress  at  the  small  surface  of  contact.     Melt- 
ing of  the  ice  therefore  occurs  at  the  places  of  contact,  and  the  cold 
thus  evolved  freezes  the  adjacent  portions  of  the  water  film,  which, 
being  at  less  than  atmospheric  pressure,  will  begin  to  freeze  at  a 
temperature  a  little  above  the  ordinary  freezing-point. 

As  regards  the  amount  of  the  force  urging  the  pieces  together,  if  two 
flat  pieces  of  ice  be  supported  with  their  faces  vertical,  and  if  they 
be  united  by  a  film  from  whose  lower  edge  water  trickles  away, 
the  hydrostatic  pressure  at  any  point  within  this  film  is  less  than 
atmospheric  by  an  amount  represented,  in  weight  of  water,  by  the 
height  of  this  point  above  the  part  from  which  water  trickles. 
If,  for  simplicity,  we  suppose  the  film  circular,  the  plates  will  be 
pressed  together  with  a  force  equal  to  the  weight  of  a  cylinder  of 
water  whose  base  is  the  film  and  whose  height  is  the  radius. 

239.  Apparent  Plasticity  of  Ice.     Motion  of  Glaciers. — A  glacier 
may  be  described  in  general   terms  as  a  mass  of  ice  deriving   its 
origin  from  mountain  snows,  and  extending  from   the  snow-fields 
along  channels  in  the  mountain  sides  to  the  valleys  beneath. 

The  first  accurate  observations  on  the  movements  of  glaciers  were 
made  in  1842,  by  the  late  Professor  (afterwards  Principal)  J.  T>. 
Forbes,  who  established  the  fact  that  glaciers  descend  along  their 
beds  with  a  motion  resembling  that  of  a  pailful  of  mortar  poured 
into  a  sloping  trough;  the  surface  moving  faster  than  the  bottom 


MOTION   OF   GLACIERS.  315 

and  the  centre  faster  than  the  sides.  He  summed  up  his  view  by 
saying,  "  A  glacier  is  an  imperfect  fluid,  or  a  viscous  body  which  is 
urged  down  slopes  of  a  certain  inclination  by  the  mutual  pressure  of 
its  parts." 

This  apparent  viscosity  is  explained  by  the  principles  of  §  237A. 
According  to  these  principles  the  ice  should  melt  away  at  the  places 
where  stress  is  most  severe,  an  equivalent  quantity  of  ice  being 
formed  elsewhere.  The  ice  would  thus  gradually  yield  to  the  ap- 
plied forces,  and  might  be  moulded  into  new  forms,  without  undergoing 
rupture.  Breaches  of  continuity  might  be  produced  in  places  where 
the  stress  consisted  mainly  of  a  pull,  for  the  pull  would  lower  the 
freezing-point,  and  thus  indirectly  as  well  as  directly  tend  to  produce 
ruptures,  in  the  form  of  fissures  transverse  to  the  direction  of  most 
intense  pull.  The  effect  of  violent  compression  in  any  direction  would, 
on  the  other  hand,  be,  not  to  crack  the  ice,  but  to  melt  a  portion  of 
its  interior  sufficient  to  relieve  the  pressure  in  the  particular  part 
affected,  and  to  transfer  the  excess  of  material  to  neighbouring  parts, 
which  must  in  their  turn  give  way  in  the  same  gradual  manner. 

In  connection  with  this  explanation  it  is  to  be  observed  that  the 
temperature  of  a  glacier  is  always  about  0°G,  and  that  its  structure 
is  eminently  porous  and  permeated  with  ice-cold  water.  These  are 
conditions  eminently  favourable  (the  former,  but  not  the  latter,  being 
essential)  to  the  production  of  changes  of  form  depending  on  the 
lowering  of  the  melting-point  by  stresses. 

This  explanation  is  due  to  Professor  J.  Thomson1  (British  Associa- 
tion Report,  1857).  Professor  Tyndall  had  previously  attempted  to 
account  for  the  phenomena  of  glacier  motion  by  supposing  that  the 
ice  is  fractured  by  the  forces  to  which  it  is  subjected,  and  that  the 
broken  pieces,  after  being  pushed  into  their  new  positions,  are  united 
by  regelation.  In  support  of  this  view  he  performed  several  very 
interesting  and  novel  experiments  on  the  moulding  of  ice  by  pres- 
sure, such  as  striking  medals  of  ice  with  a  die,  and  producing  a  clear 
transparent  cake  of  ice  by  ^powerfully  compressing  broken  pieces  in 
a  boxwood  mould  (Fig.  231). 

Interesting  experiments  on  the  plasticity  of  ice  may  be  performed 
by  filling  an  iron  shell  with  water  and  placing  it  in  a  freezing  mix- 

1  If  it  should  be  objected  that  the  lowering  of  the  melting-point  by  stress  is  too  insignifi- 
cant to  produce  the  vast  effects  here  attributed  to  it,  the  answer  is  that,  when  ice  and 
water  are  present  together,  the  slightest  difference  is  sufficient  to  determine  which  portion 
of  the  water  shall  freeze,  or  which  portion  of  the  ice  shall  melt.  In  default  of  a  more 
powerful  cause,  those  portions  of  ice  which  are  most  stressed  will  melt  first. 


316 


FUSION   AND   SOLIDIFICATION. 


ture,  leaving  the  aperture  open.  As  the  water  freezes,  a  cylinder 
of  ice  will  be  gradually  protruded.  This  experiment  is  due  to  Mr. 
Christie.  Professor  Forbes  obtained  a  similar  result  by  using  a  very 


Fig.  231. — Ice  Moulded  by  Pressure. 

strong  glass  jar;  and  by  smearing  the  interior,  just  below  the  neck, 
with  colouring  matter,  he  demonstrated  that  the  external  layer  of 
ice  which  was  first  formed,  slid  along  the  glass  as  the  freezing  pro- 
ceeded, until  it  was  at  length  protruded  beyond  the  mouth. 

In  the  experiments  of  Major  Williams,  described  in  §  23G,  it  is  pro- 
bable that  much  of  the  water  remained  unfrozen  until  its  pressure 
was  relieved  by  the  bursting  of  the  shells. 


CHAPTER    XXV. 


EVAPORATION. 


240.  Transformation  into  the  State  of  Vapour. — The  majority  of 
liquids,  when  left  to  themselves  in   contact  with  the  atmosphere, 
gradually  pass  into  the  state  of  vapour  and  disappear.     This  pheno- 
menon occurs  much  more  rapidly  with  some  liquids  than  with  others, 
and  those  which  evaporate  most  readily  are  said  to  be  the  most 
volatile.     Thus,  if  a  drop  of  ether  be  let  fall  upon  any  substance,  it 
disappears    almost    instantaneously;    alcohol    also  evaporates  very 
quickly,  but  water  requires  a  much  longer  time  for  a  similar  trans- 
formation.    The  change  is  in  all  cases  accelerated  by  an  increase  of 
temperature ;  in  fact,  when  we  dry  a  body  before  the  fire,  we  are 
simply  availing  ourselves  of  this  property  of  heat  to  hasten  the 
evaporation  of  the  moisture  of  the  body.     Evaporation  may  also 
take  place  from  solids.      Thus  camphor,  iodine,  and  several  other 
substances  pass  directly  from  the  solid  to  the  gaseous  state,  and  we 
shall  see  hereafter  that  the  vapour  of  ice  can  be  detected  at  tem- 
peratures far  below  the  freezing-point. 

Evaporation,  unlike  fusion,  occurs  over  a  very  wide  range  of  tem- 
perature. There  appears,  however,  to  be  a  temperature  for  each 
substance,  below  which  evaporation,  if  it  exist  at  all,  cannot  be 
detected.  This  is  the  case  with  mercury  at  0°  C.,  and  with  sulphuric 
acid  at  ordinary  atmospheric  temperatures. 

241.  Vapour,  Gas. — The  words  gas  and  vapour  have  no  essential 
difference  of  meaning.     A  vapour  is  the  gas  into  which  a  liquid  is 
changed  by  evaporation.     Every  gas  is  probably  the  vapour  of  a 
certain  liquid.     The  word  vapour  is  especially  applied  to  the  gaseous 
condition  of  bodies  which  are  usually  met  with  in  the  liquid  or  solid 
state,  as  water,  sulphur,  &c.;  while  the  word  gas  generally  denotes  a 
body  which,  under  ordinary  conditions,  is  never  found  in  any  state 


318  EVAPORATION. 

out  the  gaseous.  There  are  a  few  gases  which  experimenters  have 
hitherto  been  unable  to  obtain  under  any  other  form.  These  are 
oxygen,  hydrogen,  nitrogen,  nitric  oxide,  carbonic  oxide,  and  marsh 
gas ;  they  are  sometimes  called  permanent  gases. 

242.  Elastic  Force  of  Vapours.  Maximum  Tension. — The  char- 
acteristic property  of  gases  is  their  expansibility  or  elastic  force.1 
This  may  be  exemplified  in  the  case  of  vapours  by  the  following 
experiment. 

A  glass  globe  A  (Fig,  232)  is  fitted  with  a  metal  cap  provided  with 
two  openings,  one  of  which  can  be  made  to  communicate  with  a 
mercurial  manometer,  while  the  other  is  furnished  with  a  stop-cock  R. 
The  globe  is  first  exhausted  of  air  by  establishing  communication 
through  R  with  an  air-pump.  The  mercury  rises  in  the  left-hand 
and  falls  in  the  right-hand  branch  of  the  manometer;  the  final  dif- 
ference of  level  in  the  two  branches  differing  from  the  height  of  the 
barometer  only  by  the  very  small  quantity  representing  the  tension 
of  the  air  left  behind  by  the  machine.  The  stop-cock  R  is  then 
closed,  and  a  second  stop-cock  R'  surmounted  by  a  funnel  is  fixed 
above  it.  The  hole  in  this  second  stop-cock,  instead  of  going  quite 
through  the  metal,  extends  only  half-way,  so  as  merely  to  form  a 
cavity.  This  cavity  serves  to  introduce  a  liquid  into  the  globe, 
without  any  communication  taking  place  between  the  globe  and  the 
external  air.  For  this  purpose  we  have  only  to  fill  the  funnel  with 
a  liquid,  to  open  the  cock  R,  and  to  turn  that  at  R'  backwards  and 
forwards  several  times.  It  will  be  found,  that  after  the  introduction 
of  a  small  quantity  of  liquid  into  the  globe,  the  mercurial  column 
begins  to  descend  in  the  left  branch  of  the  manometer,  thus  in- 
dicating an  increase  of  elastic  force.  This  elastic  force  goes  on  in- 
creasing as  a  greater  quantity  of  liquid  is  introduced  into  the  globe ; 
and  as  no  liquid  is  visible  in  the  globe,  we  must  infer  that  it  eva- 
porates as  fast  as  it  is  introduced,  and  that  the  fall  of  the  mercurial 
column  is  caused  by  the  elastic  force  of  the  vapour  thus  formed. 

This  increase  of  pressure,  however,  does  not  go  on  indefinitely. 
After  a  time  the  difference  of  level  in  the  two  branches  of  the  mano- 
meter ceases  to  increase,  and  a  little  of  the  unevaporated  liquid  may 
be  seen  in  the  globe,  which  increases  in  quantity  as  more  liquid  is 
introduced.  From  this  important  experiment  we  conclude  that  there 
is  a  limit  to  the  quantity  of  vapour  which  can  be  formed  at  a  given 
temperature  in  an  empty  space.  When  this  limit  is  reached,  the 

1  The  names  pressure,  tension,  and  elastic  jorce,  are  used  interchangeably. 


FORMATION    OF   VAPOUES. 


319 


space  is  said  to  be  saturated,  and  the  vapour  then  contained  in  it  is 
at  maximum  tension,  and  at  maximum  density.  It  evidently  fol- 
lows from  this  that  if  a  quantity  of  vapour  at  less  than  its  maximum 
tension  be  inclosed  in  a  given  space,  and  then  compressed  at  constant 


Fig.  232. — Apparatus  for  studying  the  Formation  of  Vapours. 

temperature,  its  tension  and  density  will  increase  at  first,  but  that 
after  a  time  a  point  will  be  reached  when  further  compression,  in- 
stead of  increasing  the  density  of  the  vapour,  will  only  cause  some  of 
it  to  pass  into  the  liquid  state.  This  last  result  may  be  directly 
verified  by  the  following  experiment.  A  barometric  tube  a  b  (Fig. 
233)  is  filled  with  mercury,  with  the  exception  of  a  small  space,  into 
which  a  few  drops  of  ether  are  introduced,  care  having  first  been 


320 


EVAPORATION. 


taken  to  expel  any  bubbles  of  air  which  may  have  remained  ad- 
hering to  the  mercury.  The  tube  is  then  inverted  in  the  deep  bowl 
MN,  when  the  ether  ascends  to  the  surface  of  the  mercury,  is  there 
converted  into  vapour,  and  produces  a  sensible  depression  of  the 

mercurial  column.  If  the  quantity  of  ether 
be  sufficiently  small,  and  if  the  tube  be 
kept  sufficiently  high,  no  liquid  will  be 
perceived  in  the  space  above  the  mercury ; 
this  space,  in  fact,  is  not  saturated.  The 
tension  of  the  vapour  which  occupies  it  is 
given  by  the  difference  between  the  height 
of  the  column  in  the  tube  and  of  a  baro- 
meter placed  beside  it.  If  the  tube  be 
gradually  lowered,  this  difference  will  at 
first  be  seen  to  increase,  that  is,  the  tension 
of  the  vapour  of  ether  increases;  but  if 
we  continue  the  process,  a  portion  of  liquid 
ether  will  be  observed  to  collect  above  the 
mercury,  and  after  this,  if  we  lower  the 
tube  any  further,  the  height  of  the  mer- 
cury in  it  remains  invariable.  The  only 
effect  is  to  increase  the  quantity  of  liquid 
deposited  from  the  vapour.1 

243.  Influence  of  Temperature  on  the 
Maximum  Tension. — Returning  now  to 
the  apparatus  represented  in  Fig.  232,  sup- 
pose that  some  of  the  liquid  remains  un- 
evaporated  in  the  bottom  of  the  globe,  and 
let  the  globe  be  subjected  to  an  increase 
of  temperature.  An  increase  of  elastic 
force  will  at  once  be  indicated  by  the  man- 
ometer, while  the  quantity  of  liquid  will 
be  diminished.  The  maximum  tension  of 

a  vapour,  therefore,  and  also  its  maximum  density,  increase  with  the 
temperature ;  and  consequently,  in  order  to  saturate  a  given  space, 
a  quantity  of  vapour  is  required  which  increases  with  the  tempera- 
ture. In  a  subsequent  chapter  we  shall  give  the  results  of  experi- 

1  Strictly  speaking,  there  will  be  a  slight  additional  depression  of  the  mercurial  column 
due  to  the  weight  of  the  liquid  thus  deposited  on  its  summit ;  but  this  effect  will  generally 
be  very  small,  as  the  vapour  occupies  much  more  space  than  the  liquid  which  it  yields. 


Pig.  233.— Maximum  Tension  of 
Vapours. 


SATURATION  AT  DIFFERENT  TEMPERATURES. 


321 


merits  on  the  maximum  tension  of  aqueous  vapour  at  different  tem- 
peratures, and  it  will  be  seen  that  the  increase  is  exceedingly  rapid. 
Fig.  234  is  a  graphical  representation  of  the  rate  at  which  the 
maximum  density  of  a  vapour  increases  with  the  temperature. 
Lengths  are  laid  off  on  the  base-line  AB,  to  represent  temperatures 
from  —20°  to  -f-35°C.,  and  ordinates  are  erected  at  every  fifth  de- 


+10° 


300. 


200. 


100. 


+20° 


Fig.  234.— Saturation  at  different  Temperatures. 

gree,  proportional  to  the  weights  of  vapour  required  to  saturate  the 
same  space  at  different  temperatures.  The  curve  CD,  drawn  through 
the  extremities  of  these  ordinates,  is  the  curve  of  vapour-density  as 
a  function  of  temperature.  The  figures  on  the  right  hand  indicate 
the  number  of  grammes  of  vapour  required  to  saturate  a  cubic  metre. 

244.  Mixture  of  Gas  and  Vapour. — The  experiments  with  the 
apparatus  of  Fig.  232  may  be  repeated  after  filling  the  globe  with 
dry  air,  or  any  other  dry  gas,  and  the  results  finally  obtained  will 
be  the  same  as  with  the  exhausted  globe.  If,  as  before,  we  introduce 
successive  small  quantities  of  a  liquid,  it  will  be  converted  into  vapour, 
and  the  pressure  will  go  on  increasing  till  saturation  is  attained;  the 
elastic  force  of  vapour  will  then  be  found  to  be  exactly  the  same  as 
in  the  case  of  the  vacuous  globe,  and  the  quantity  of  liquid  eva- 
porated will  also  be  the  same. 

There  is,  however,  one  important  difference.  In  the  vacuum  the 
complete  evaporation  of  the  liquid  is  almost  instantaneous ;  in  a  gas, 
on  the  other  hand,  the  evaporation  arid  consequent  increase  of  pres- 
sure proceed  with  comparative  slowness;  and  the  difference  between 

21 


322  EVAPORATION. 

the  two  cases  is  more  marked  in  proportion  as  the  pressure  of  the 
gas  is  greater. 

We  may  lay  down,  then,  the  two  following  laws  for  the  mixture 
of  a  vapour  with  a  gas : — 

1.  The  weight  of  vapour  which  will  enter  a  given  space  is  the 
same  whether  this  space  be  empty  or  filled  with  gas,  provided  plenty 
of  time  be  allowed. 

2.  When  a  gas  is  saturated  with  vapour,  the  actual  tension  of  the 
mixture  is  the  sum  of  the  tensions  due  to  the  gas  and  vapour  sepa- 
rajkely;  that  is  to  say,  it  is  equal  to  the  pressure  which  the  gas  would 
exert  if  it  alone  occupied  the  ivhole  space,  plus  the  maximum  ten- 
sion of  vapour  for  the  temperature  of  the  mixture. 

This  second  law  evidently  comes  under  the  general  rule  for  deter- 
mining the  pressure  of  a  mixture  of  gases  (§  127);  and  the  same  rule 
applies  to  a  mixture  of  gas  and  vapour  when  the  quantity  of  the 
latter  falls  short  of  saturation.  Each  element  in  a  mixture  of  gases 
and  vapours  exerts  the  same  pressure  on  the  walls  of  the  containing 
vessel  as  it  would  exert  if  the  other  elements  were  removed. 

It  is  doubtful,  however,  whether  these  laws  are  rigorously  true. 
It  would  rather  appear  from  some  of  Regnault's  experiments,  that 
the  quantity  of  vapour  taken  up  in  a  given  space  is  slightly,  though 
almost  insensibly,  diminished,  as  the  density  of  the  gas  which  oc- 
cupies the  space  is  increased. 

X  245.  Liquefaction  of  Gases. — When  vapour  exists  in  the  state  of 
saturation,  any  diminution  in  the  volume  must,  if  the  temperature 
is  preserved  constant,  involve  the  liquefaction  of  as  much  of  the 
vapour  as  would  occupy  the  difference  of  volumes;  and  the  vapour 
which  remains  will  still  be  at  the  original  density  and  tension.  A 
vapour  existing  by  itself  may  therefore  be  completely  liquefied  by 
subjecting  it  to  a  pressure  exceeding,  by  ever  so  slight  an  amount, 
the  maximum  tension  corresponding  to  the  temperature,  provided 
that  the  containing  vessel  is  prevented  from  rising  in  temperature. 

Again,  if  a  vapour  at  saturation  be  subjected  to  a  fall  of  tem- 
perature, while  its  volume  remains  unchanged,  a  portion  of  it  must 
be  liquefied  corresponding  to  the  difference  between  the  density  of 
saturation  at  the  higher  and  at  the  lower  temperature.  This  opera- 
tion will  obviously  diminish  the  tension,  since  this  will  now  be  the 
maximum  tension  corresponding  to  the  lower  instead  of  to  the 
higher  temperature. 

There  are  therefore  two  distinct  means  of  liquefying  a  vapour — 


LIQUEFACTION   OF   GASES. 


823 


Fig.  235.— Liquefaction  of  Sulphurous  Acid. 


increase  of  pressure,  and  lowering  of  temperature.     They  are  em- 
ployed sometimes  separately,  and  sometimes  in  conjunction. 

Fig.  235  represents  the  apparatus  usually  employed  for  obtaining 
sulphurous  acid  in  the 
liquid  state.  The  gas, 
which  is  generated  in  a 
glass  globe,  passes  first 
into  a  washing -bottle, 
then  through  a  drying- 
tube,  and  finally  into  a 
tube  surrounded  with  a 
freezing  mixture  of  snow 
and  salt. 

Pouillet's  apparatus,  de- 
scribed in  §  120,  serves  to  liquefy  most  gases  by  means  of  compression 

In  order  to  ascertain  the  pressures  at  which  liquefaction  takes 
place,  or,  in  other  words,  the  maximum  tensions  of  gases,  one  of  the 
tubes  in  that  apparatus  is  replaced  by  a  shorter  tube,  containing 
atmospheric  air,  and  serving  as  a  manometer. 

By  this  means  Pouillet  has  found  that,  at  the  temperature  of  10°  C., 
sulphurous  acid  is 
liquefied  by  a  pressure 
of  2J  atmospheres, 
nitrous  oxide  by  a 
pressure  of  43,  and 
carbonic  acid  by  a 
pressure  of  45  atmo- 
spheres. 

246.  Faraday's  Me- 
thod.— Faraday,  who 
was  the  first  to  con- 
duct methodical  ex- 
periments on  the 
liquefaction  of  gases, 
employed,  in  the  first 
instance,  the  simple 
apparatus  represent- 
ed in  Fig.  236.  It 
consists  of  a  very  strong  bent  glass  tube,  one  end  of  which  contains 
ingredients  which  evolve  the  gas  on  the  application  of  heat,  while 


Fig.  236. — Faraday's  Apparatus. 


324 


EVAPORATION. 


the  other  is  immersed  in  a  freezing  mixture.  The  pressure  produced 
by  the  evolution  of  the  gas  in  large  quantity  in  a  confined  space, 
combines  with  the  cold  of  the  freezing  mixture  to  produce  liquefac- 
tion of  the  gas,  and  the  liquid  accordingly  collects  in  the  cold  end  of 
the  tube. 

Thilorier,  about  the  year  1 834,  invented  the  apparatus  represented 
in  Fig.  237,  which  is  based  on  this  method  of  Faraday,  and  is  in- 
tended for  liquefying  carbonic  acid  gas.  This  operation  requires  the 
enormous  pressure  of  about  fifty  atmospheres  at  ordinary  tempera- 
tures. If  a  slight  rise  of  temperature  occur  from  the  chemical  actions 
attending  the  production  of  the  gas,  a  pressure  of  75  or  80  atmo- 
spheres may  not  improbably  be  required.  Hence  great  care  is  neces- 
sary in  testing  the  strength  of  the  metal  employed  in  the  construc- 
tion of  the  apparatus.  It  was  formerly  made  of  cast  iron,  and 


Fig.  237.— Thilorier's  Apparatus. 

strengthened  by  wrought-iron  hoops;  but  the  construction  has  since 
been  changed  on  account  of  a  terrible  explosion,  which  cost  the  life 
of  one  of  the  operators.  At  present  the  vessels  are  formed  of  three 
parts ;  the  inner  one  of  lead,  the  next  e,  which  completely  envelops 
this,  of  copper,  and  finally,  the  hoops  //  of  wrought  iron  (Fig.  237), 
which  bind  the  whole  together.  The  apparatus  consists  of  two  dis- 


LIQUEFACTION   OF   GASES.  325 

tinct  reservoirs.  In  the  generator  C  is  placed  bicarbonate  of  soda, 
and  a  vertical  tube  a,  open  at  top,  containing  sulphuric  acid.  By 
imparting  an  oscillatory  movement  to  the  vessel  about  the  two  pivots 
which  support  it  near  the  middle,  the  sulphuric  acid  is  gradually 
spilt,  and  the  carbonic  acid  is  evolved,  and  becomes  liquid  in  the 
interior.  The  generator  is  then  connected  with  the  condenser  C'  by 
the  tube  t,  and  the  stop-cocks  R  and  B/  are  opened.  As  soon  as  the 
two  vessels  are  in  communication,  the  liquid  carbonic  acid  passes  into 
the  condenser,  which  is  at  a  lower  temperature  than  the  generator, 
and  represents  the  cold  branch  of  Faraday's  apparatus.  The  gene- 
rator can  then  be  disconnected  and  recharged,  and  thus  several  pints 
of  liquid  carbonic  acid  may  be  obtained. 

In  the  foregoing  methods,  the  pressure  which  produces  liquefaction 
is  furnished  by  the  evolution  of  the  gas  itself. 

In  some  other  forms  of  apparatus  the  pressure  is  obtained  by  the 
use  of  one  or  more  compression-pumps,  which  force  the  gas  from  the 
vessel  in  which  it  is  generated  into  a  second  vessel,  which  is  kept  cool 
either  by  ice  or  a  freezing  mixture.  The  apparatus  of  this  kind 
which  is  most  extensively  used  is  that  devised  by  Bianchi.  It  con- 
sists of  a  compression-pump  driven  by  a  crank  furnished  with  a  fly- 
wheel, and  turned  by  hand. 

Faraday,  in  his  later  experiments,  employed  two  pumps,  the  first 
having  a  piston  of  an  inch,  and  the  second  of  only  half  an  inch  dia- 
meter. The  first  pump  in  the  earlier  stage  of  the  operation  forced 
the  gas  through  the  second  into  the  receiver.  In  the  later  stage  the 
second  pump  was  also  worked,  so  as  to  force  the  gas  already  con- 
densed to  10,  15,  or  20  atmospheres  into  the  receiver  at  a  much 
higher  pressure.  The  receiver  was  a  tube  of  green  bottle-glass,  and 
was  immersed  in  a  very  intense  freezing  mixture,  consisting  of  solid 
carbonic  acid  and  ether,  the  cooling  effect  being  sometimes  increased 
by  exhausting  the  air  and  vapour  from  the  vessel  containing  the 
freezing  mixture,  so  as  to  promote  more  rapid  evaporation. 

246  A.  Continuity  of  the  Liquid  and  Gaseous  States. — Remarkable 
results  were  obtained  by  Cagniard  de  la  Tour1  by  heating  volatile 
liquids  (alcohol,  petroleum,  and  sulphuric  ether)  in  closed  tubes  of 
great  strength,  and  of  capacity  about  double  the  volume  of  the 
inclosed  liquid.  At  certain  temperatures  (36°  C.  for  alcohol,  and  42° 
for  ether)  the  liquid  suddenly  disappeared,  becoming  apparently  con- 
verted into  vapour. 

1  Ann.  de  Chim.  II.  xxi. 


326  EVAPOEATION. 

Drion,1  by  similar  experiments  upon  hydrochloric  ether,  hyponitric 
acid,  and  sulphurous  acid,  showed — 

1.  That  the  coefficients  of  apparent  expansion  of  these  liquids 
increase  rapidly  with  the  temperature. 

2.  That  they  become  equal  to  the  coefficient  of  expansion  of  air, 
at  temperatures  much  lower  than  those  at  which  total  conversion 
into  vapour  occurs. 

3.  That  they  may  even  become  double  and  more  than  double  the 
coefficient  of  expansion  of  air;  for  example,  at  130°C.  the  coefficient 
of  expansion  of  sulphurous  acid  was  '009571. 

Thilorier  had  previously  shown  that  the  expansion  of  liquid  car- 
bonic acid  between  the  temperatures  0°  and  30°  C.  is  four  times  as 
great  as  that  of  air. 

Drion  further  observed,  that  when  the  temperature  was  raised 
very  gradually  to  the  point  of  total  vaporization,  the  free  surface  lost 
its  definition,  and  was  replaced  by  a  nebulous  zone  without  definite 
edges  and  destitute  of  reflecting  power.  This  zone  increased  in  size 
both  upwards  and  downwards,  but  at  the  same  time  became  less 
visible,  until  the  tube  appeared  completely  empty.  The  same 
appearances  were  reproduced  in  inverse  order  on  gradually  cooling 
the  tube. 

When  the  liquid  was  contained  in  a  capillary  tube,  or  when  a 
capillary  tube  was  partly  immersed  in  it,  the  curvature  of  the  meniscus 
and  the  capillary  elevation  decreased  as  the  temperature  rose,  until 
at  length,  just  before  the  occurrence  of  total  vaporization,  the  surface 
became  plane,  and  the  level  was  the  same  within  as  without  the  tube. 

Dr.  Andrews,  by  a  .series  of  elaborate  experiments  on  carbonic 
acid,  with  the  aid  of  an  apparatus  which  permitted  the  pressure  and 
temperature  to  be  altered  independently  of  each  other,  has  shown 
that  at  temperatures  above  31°  C.  this  gas  cannot  be  liquefied,  but, 
when  subjected  to  intense  pressure,  becomes  reduced  to  a  condition 
in  which,  though  homogeneous,  it  is  neither  a  liquid  nor  a  gas. 
When  in  this  condition,  lowering  of  temperature  under  constant  pres- 
sure will  reduce  it  to  a  liquid,  and  diminution  of  pressure  at  constant 
temperature  will  reduce  it  to  a  gas;  but  in  neither  case  can  any  breach 
of  continuity  be  detected  in  the  transition. 

On  the  other  hand,  at  temperatures  below  31°,  the  substance 
remains  completely  gaseous  until  the  pressure  reaches  a  certain  limit 
depending  on  the  temperature,  and  any  pressure  exceeding  this  limit 

1  Ann.  de  Chim.  III.  Ivi. 


THE   CRITICAL   TEMPERATURE.  327 

causes  liquefaction  to  commence  and  to  continue  till  the  whole  of  the 
gas  is  liquefied,  the  boundary  between  the  liquefied  and  unliquefied 
portions  being  always  sharply  defined. 

The  temperature  31°C.,  or  more  exactly  30'92°C.  (877°  F.),  may 
therefore  be  called  the  critical  temperature  for  carbonic  acid ;  and  it 
is  probable  that  every  other  substance,  whether  usually  occurring  in 
the  gaseous  or  in  the  liquid  form,  has  in  like  manner  its  own  critical 
temperature.  Dr.  Andrews  found  that  nitrous  oxide,  hydrochloric 
acid,  ammonia,  sulphuric  ether,  and  sulphuret  of  carbon,  all  exhibited 
critical  temperatures,  which,  in  the  case  of  some  of  these  substances, 
were  above  100°C. 

It  is  probable  that,  in  the  experiments  of  Cagniard  de  la  Tour  and 
Drion,  the  so-called  total  conversion  into  vapour  was  really  conver- 
sion into  the  intermediate  condition. 

The  continuous  conversion  of  a  gas  into  a  liquid  may  be  effected 
by  first  compressing  it  at  a  temperature  above  its  critical  tempera- 
ture, until  it  is  reduced  to  the  volume  which  it  will  occupy  when 
liquefied,  and  then  cooling  it  below  the  critical  point. 

The  continuous  conversion  of  a  liquid  into  a  gas  may  be  obtained 
by  first  raising  it  above  the  critical  temperature  while  kept  under 
pressure  sufficient  to  prevent  ebullition,  and  afterwards  allowing  it 
to  expand. 

When  a  substance  is  a  little  above  its  critical  temperature,  and 
occupies  a  volume  which  would,  at  a  lower  temperature,  be  com- 
patible with  partial  liquefaction,  very  great  changes  of  volume  are 
produced  by  very  slight  changes  of  pressure. 

On  the  other  hand,  when  a  substance  is  at  a  temperature  a  little 
below  its  critical  point,  and  is  partially  liquefied,  a  slight  increase  of 
temperature  leads  to  a  gradual  obliteration  of  the  surface  of  demarca- 
tion between  the  liquid  and  the  gas;  and  when  the  whole  has  thus 
been  reduced  to  a  homogeneous  fluid,  it  can  be  made  to  exhibit  an 
appearance  of  moving  or  flickering  strise  throughout  its  entire  mass 
by  slightly  lowering  the  temperature,  or  suddenly  diminishing  the 
pressure. 

The  apparatus  employed  in  these  remarkable  experiments,  which 
are  described  in  the  Bakerian  Lecture  (Phil.  Trans.  1 869),  is  shown 
in  Fig.  237A,  where  cc  are  two  capillary  glass  tubes  of  great  strength, 
one  of  them  containing  the  carbonic  acid  or  other  gas  to  be  experi- 
mented on,  the  other  containing  air  to  serve  as  a  manometer.  These 
are  connected  with  strong  copper  tubes  dd,  of  larger  diameter,  con- 


328 


EVAPORATION. 


taining  water,  and  communicating  with  each  other  through  a  6,  the 
water  being  separated  from  the  gases  by  a  column  of  mercury  oc- 
cupying the  lower  portion  of  each 
capillary  tube.  The  steel  screws  ss 
are  the  instruments  for  applying 
pressure.  By  screwing  either  of 
them  forward  into  the  water,  the 
contents  of  both  tubes  are  com- 
pressed, and  the  only  use  of  having 
two  is  to  give  a  wider  range  of 
compression.  A  rectangular  brass 
case  (not  shown  in  the  figure),  closed 
before  and  behind  with  plate- glass, 
surrounds  each  capillary  tube,  and 
allows  it  to  be  maintained  at  any 
required  temperature  by  the  flow 
of  a  stream  of  water. 

247.  Latent  Heat  of  Vaporization. 
Cold  produced  by  Evaporation. — The 
passage  from  the  liquid  to  the  gas- 
eous state  is  accompanied  by  the 
disappearance  of  a  large  quantity  of 

heat.  Whenever  a  liquid  evaporates  without  the  application  of  heat, 
a  depression  of  temperature  occurs.  Thus, 
for  instance,  if  any  portion  of  the  skin  be 
kept  moist  with  alcohol  or  ether,  a  decided 
sensation  of  cold  is  felt.  Water  produces 
the  same  effect  in  a  smaller  degree,  be- 
cause it  evaporates  less  rapidly. 

The  heat  which  thus  disappears  in 
virtue  of  the  passage  of  a  liquid  into  the 
gaseous  condition,  is  called  the  latent  heat 
of  vaporization.  Its  amount  varies  ac- 
cording to  the  temperature  at  which  the 
change  is  effected,  and  it  is  exactly  re- 
stored when  the  vapour  returns  to  the 
liquid  form,  provided  that  both  changes 
have  been  effected  at  the  same  tempera- 
ture. Its  amount  for  vapour  of  water  at  the  temperature  100°  C. 
is  536°;  that  is  to  say,  the  quantity  of  heat  which  disappears  in  the 


Fig.  237  A. — Andrews'  Apparatus. 


Fig.  238. — Leslie's  Experiment. 


LATENT  HEAT  OF  VAPORIZATION. 


329 


evaporation  of  a  pound  of  water  at  this  temperature,  and  which 
reappears  in  the  condensation  of  a  pound  of  steam  at  the  same  tem- 
perature, would  be  sufficient  to  raise  the  temperature  of  536  pounds 
of  water  from  0°  to  1°. 

The  latent  heat  of  vaporization  plays  an  important  part  in  the 
beating  of  buildings  by  steam.      A   pound   of   steam   at  100°,  in 


Fig.  239.— Carre's  Apparatus. 

becoming  reduced  to  water  at  30°,  gives  out  as  much  heat  as  about 
8|  Ibs.  of  water  at  100°  in  cooling  down  to  the  same  temperature. 

248.  Leslie's  Experiment. — Water  can  be  easily  frozen  by  the  cold 
resulting  from  its  own  evaporation,  as  was  first  shown  by  Leslie  in 
a  celebrated  experiment.  A  small  capsule  (Fig.  238)  of  copper  is 


330 


EVAPORATION. 


taken,  containing  a  little  water,  and  is  placed  above  a  vessel  con- 
taining strong  sulphuric  acid.  The  whole  is  placed  under  the  receiver 
of  an  air-pump,  which  is  then  exhausted.  The  water  evaporates  with 
great  rapidity,  the  vapour  being  absorbed  by  the  sulphuric  acid  as 
i'ast  as  it  is  formed,  and  ice  soon  begins  to  appear  on  the  surface. 
The  experiment  is,  however,  rather  difficult  to  perform  successfully. 
This  arises  from  various  causes. 

In  the  first  place,  the  vapour  of  water  which  occupies  the  upper 
part  of  the  receiver  is  only  imperfectly  absorbed ;  and,  in  the  second 
place,  as  the  upper  layer  of  the  acid  becomes  diluted  by  absorbing 
the  vapour,  its  affinity  for  water  rapidly  diminishes. 

These  obstacles  have  been  removed  by  an  apparatus  invented  ly 
M.  Carre,  which  enables  us  to  obtain  a  considerable  mass  of  ice  in  a 
few  minutes.  It  consists  (Fig.  239)  of  a  leaden  reservoir  containing 
sulphuric  acid.  At  one  extremity  is  a  vertical  tube,  the  end  of  which 
is  bent  over  and  connected  with  a  flask  containing  water.  The  other 
extremity  of  the  reservoir  communicates  with  an  air-pump,  to  the 
handle  of  which  is  fitted  a  metallic  rod,  which  drives  an  agitator 
immersed  in  the  acid.  By  this  means  the  surface  of  the  acid  is  con- 
tinually renewed,  absorption  takes  place  with  regularity,  and  the  water 
is  rapidly  frozen. 

249.  Cryophorus. — Wollaston's  cryophorus  (Fig.  240)  consists  of  a 
bent  tube  with  a  bulb  at  each  end.  It  is  partly  filled  with  water, 

and  hermetically  sealed  while  the 
liquid  is  in  ebullition,  thus  expelling 
the  air. 

When  an  experiment  is  to  be  made, 
all  the  liquid  is  passed  into  the  bulb 
B,  and  the  bulb  A  is  plunged  into  a 
freezing  mixture,  or  into,  pounded  ice. 
The  cold  condenses  the  vapour  in  A,. 
and  thus  produces  rapid  evaporation 
of  the  water  in  B.  In  a  short  time 
needles  of  ice  appear  on  the  surface  of 
the  liquid. 

250.  Freezing  of  Water  by  the  Eva- 
poration of  Ether. — Water  is  poured 
into  a  glass  tube  dipped  into  ether, 
which  is  contained  in  a  glass  vessel  for  the  purpose  (Fig.  241).  By 
means  of  a  pair  of  bellows  a  current  of  air  is  made  to  pass  through 


Fig.  240.— Cryophorus. 


FREEZING   OF   MERCURY. 


331 


the  ether;  evaporation  is  quickly  produced,  and  at  the  end  of  a  few 
minutes  the  water  in  the  tube  is  frozen. 


Fig.  241.— Freezing  of  Water  by  Evaporation  of  Ether. 

If,  instead  of  promoting  evaporation  of  the  ether  by  means  of  a 
current  of  air,  the  vessel  were  placed  under  the  exhausted  receiver 
of  an  air-pump,  a  much  greater  fall  of  temperature  would  be  ob- 
tained, and  even  mercury  might  easily  be  frozen.  This  experiment, 
however,  is  injurious  to  the  pump,  owing  to  the  sol- 
vent action  of  the  ether  on  the  oil  with  which  the 
valves  and  other  moving  parts  are  lubricated. 

251.  Freezing  of  Mercury  by  means  of  Sulphurous 
Acid. — Mercury  may  be  frozen  by  means  of  liquid 
sulphurous  acid,  which  is  much  more  volatile  than 
ether.  In  order  to  escape  the  suffocating  action  of  the 
gas,  the  experiment  is  performed  in  the  following 
manner: — 

Into  a  glass  vessel  (Fig.  242)  are  poured  successively 
mercury  and  liquid  sulphurous  acid.     The  vessel  is 
closed  by  an  india-rubber  stopper,  in  which  two  glass 
tubes  are  fitted.     One  of  these  dips  to  the  bottom  of  the  sulphur- 
ous acid,  and  is  connected  at  its  outer  end  with  a  bladder  full  of 


Fig.  242. 

Freezing  of  Mercury 
by  Evaporation  of 
Sulphurous  Acid. 


332 


EVAPORATION. 


air.  Air  is  passed  through  the  liquid  by  compressing  the  bladder, 
and  escapes,  charged  with  vapour,  through  the  second  opening, 
which  is  fitted  with  an  india-rubber  tube  leading  to  the  open  air. 
Evaporation  proceeds  with  great  rapidity,  and  the  mercury  soon 
freezes. 

252.  Carre's  Apparatus. — The  apparatus  invented  some  years  ago 
by  M.  Carre  for  making  ice  is  another  instance  of  the  application  of 
cold  produced  by  evaporation.  It  consists  (Figs.  243  and  244)  of  two 
parts,  a  boiler  and  a  cooler.  The  boiler  is  of  wrought  iron,  arid  is  so 
constructed  as  to  give  a  very  large  heating  surface.  It  is  three- 


Fig.  243. 


Carry's  Apparatus. 


quarters  filled  with  a  saturated  solution  of  ammonia,  which  contains 
from  six  to  seven  hundred  times  its  volume  of  gas.  The  cooler  is  of 
an  annular  form,  and  in  the  central  space  is  placed  a  vessel  contain- 
ing the  water  to  be  frozen.  In  the  sides  of  the  cooler  are  a  number 
of  small  cells,  the  object  of  which  is  to  increase  the  surface  of  con- 
tact of  the  metal  with  the  liquid. 

In  the  first  part  of  the  experiment,  which  is  represented  in  the 
figure,  the  boiler  is  placed  upon  a  fire,  and  the  temperature  raised  to 
1 30°,  while  the  cooler  is  surrounded  with  cold  water.  Ammoniacal 
gas  is  given  off,  passes  into  the  cooler  by  the  valve  s'  opening  up- 
wards, and  is  condensed  in  the  numerous  cells  above  mentioned. 
This  first  part  of  the  operation,  in  the  small  machines  for  domestic 
use,  occupies  about  three-quarters  of  an  hour.  In  the  second  part  of 
the  operation,  the  cylindrical  vessel  containing  the  water  to  be  frozen 
is  placed  in  the  central  space ;  the  cooler  is  surrounded  with  an  envelope 
of  felt,  which  is  a  very  bad  conductor  of  heat,  and  the  boiler  is  im- 


SOLIDIFICATION   OF   CARBONIC  ACID.  333 

mersed  in  cold  water.  The  water  in  the  boiler,  as  it  cools,  is  able 
again  to  receive  and  dissolve  the  gas,  which  enters  by  the  valve  s  of 
the  bent  siphon-shaped  tube.  The  liquid  ammonia  in  the  cooler 
accordingly  evaporates  with  great  rapidity,  producing  a  fall  of  tem- 
perature which  freezes  the  water  in  the  inclosed  vessel. 

253.  Solidification  of  Carbonic  Acid. — When  a  small  orifice  is  opened 
in  a  vessel  containing  liquid  carbonic  acid,  evaporation  proceeds  so 
rapidly  that  the  cold  resulting  from  it  freezes  a  portion  of  the  vapour, 
which  takes  the  form  of  fine  snow,  and  may  be  collected  in  consider- 
able quantity. 

This  carbonic  acid  snow,  which  was  first  obtained  by  Thilorier,  is 
readily  dissolved  by  ether,  and  forms  with  it  one  of  the  most  intense 
freezing  mixtures  known.  By  immersing  tubes  containing  liquefied 
gases  in  this  mixture,  Faraday  succeeded  in  reducing  several  of  them, 
including  carbonic  acid,  cyanogen,  and  nitrous  oxide,  to  the  form  of 
clear  transparent  ice,  the  fall  of  temperature  being  aided,  in  some 
of  his  experiments,  by  employing  an  air-pump  to  promote  more  rapid 
evaporation  of  carbonic  acid  from  the  mixture.  By  the  latter  pro- 
cess he  was  enabled  to  obtain  a  temperature  of  —  1G6°  F.  (—110°  C.) 
as  indicated  by  an  alcohol  thermometer,  the  alcohol  itself  being  re- 
duced to  the  consistence  of  oil.  Despretz,  by  means  of  the  cold 
produced  by  a  mixture  of  solid  carbonic  acid,  liquid  nitrous  oxide, 
and  ether,  rendered  alcohol  so  viscid  that  it  did  not  run  out  when 
the  vessel  which  contained  it  was  inverted. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 


CHAPTER    XXVI. 


EBULLITION. 


254.  Ebullition. — When  a  liquid  contained  in  an  open  vessel  is  sub- 
jected to  a  continual  increase  of  temperature,  it  is  gradually  changed 
into  vapour,  which  is  dissipated  in  the  surrounding  atmosphere. 
This  action  is  at  first  confined  to  the  surface;  but  after  a  certain  time 

bubbles  of  vapour  are  formed  in  the  inte- 
rior of  the  liquid,  which  rise  to  the  top, 
and  set  the  entire  mass  in  motion  with 
more  or  less  vehemence,  accompanied  by  a 
characteristic  noise ;  this  is  what  is  meant 
by  ebullition  or  boiling. 

If  we  observe  the  gradual  progress  of 
this  phenomenon, — for  example,  in  a  glass 
vessel  containing  water,  we  shall  perceive 
that,  after  a  certain  time,  very  minute 
bubbles  are  given  off;  these  are  bubbles 
of  dissolved  air.  Soon  after,  at  the  bottom 
of  the  vessel,  and  at  those  parts  of  the  sides 
which  are  most  immediately  exposed  to 
the  action  of  the  fire,  larger  bubbles  of 
vapour  are  formed,  which  decrease  in  vol- 
ume as  they  ascend,  and  disappear  before 
reaching  the  surface.  This  stage  is  accom- 
panied by  a  peculiar  sound,  indicative  of 
approaching  ebullition,  and  the  liquid  is  said  to  be  singing.  The 
sound  is  probably  caused  by  the  collapsing  of  the  bubbles  as  they  are 
condensed  by  the  colder  water  through  which  they  pass.  Finally, 
the  bubbles  increase  in  number,  growing  larger  as  they  ascend,  until 
they  burst  at  the  surface,  which  is  thus  kept  in  a  state  of  agitation ; 
the  liquid  is  then  said  to  boiL 


Fig.  245.— Ebullition. 


LAWS   OF  EBULLITION.  »  335 

255.  Laws  of  Ebullition. — 1.  At  the  ordinary  pressure,  ebullition 
commences  nt  a  temperature  which  (roughly  speaking}  is  definite  for 
each  liquid. 

This  law  is  analogous  to  that  of  fusion  (§  225).  It  follows  from 
this  that  the  boiling-point  of  any  liquid  is  a  specific  element,  serving 
to  determine  its  nature. 

The  following  table  gives  the  boiling-points  of  several  liquids  at 
the  pressure  of  7GO  millimetres : — 

Sulphurous  acid, -10°C.  Spirits  of  turpentine,      .     .     .  +  130°C. 

Hydrochloric  ether,       .     .     .     .  +  11°  Phosphorus, 290° 

Common  ether, 37°  Concentrated  sulphuric  acid,   .     325° 

Alcohol, 79°  Mercury, 353C 

Distilled  water, 100°  Sulphur, 440° 

2.  The  temperature,  in  ordinary  circumstances,  remains  constant 
during  ebullition.     If  a  thermometer  be  introduced  into  the  glass 
vessel  of  Fig.  245,  the  temperature  will  be  observed  to  rise  gradually 
during  the  different  stages  preceding  ebullition;  but,  when  active 
ebullition  has  once  commenced,  no  further  variation  of  temperature 
will  be  observed.     This  phenomenon  points  to  the  same  conclusion 
as  the  cold  produced  by  evaporation. 

Since,  notwithstanding  the  continuous  action  of  the  fire,  the 
temperature  remains  constant,  the  conclusion  is  inevitable,  that  all 
the  heat  produced  is  employed  in  doing  the  work  necessary  to  change 
the  liquid  into  vapour.  The  constancy  of  temperature  during  ebulli- 
tion explains  the  fact  that  vessels  of  pewter,  tin,  or  any  other  easily 
fusible  metal,  may  be  safely  exposed  to  the  action  of  even  a  very  hot 
fire,  provided  that  they  contain  water,  since  the  liquid  remains  at  a 
temperature  of  about  100°,  and  its  contact  prevents  the  vessel  from 
over-heating. 

3.  The  elastic  force  of  the  vapour  given  of  during  ebullition  is 
equal  to  the  pressure  of  the  external  air. 

This  important  proposition  may  be  experimentally  demonstrated 
in  the  following  manner: — 

We  take  a  bent  tube  A,  open  at  the  longer  extremity,  and  closed 
at  the  shorter.  The  short  branch  is  filled  with  mercury,  all  but  a 
small  space  containing  water;  in  the  long  branch  the  mercury  stands 
a  little  higher  than  the  bend.  Water  is  now  boiled  in  a  glass  vessel, 
and,  during  ebullition,  the  bent  tube  is  plunged  into  the  steam. 
The  water  occupying  the  upper  part  of  the  short  branch  is  partially 
converted  into  steam,  the  mercury  falls,  and  it  assumes  the  same 


3.36 


EBULLITION. 


level  in  both  branches.     Thus  the  pressure  exerted  by  the  atmosphere 
at  the  open  extremity  of  the  tube  is  exactly  equal  to  that  exerted  by 

the  vapour  formed  by  water  in 
ebullition. 

256.  Theory  of  Ebullition. — 
This  latter  circumstance  supplies 
the  true  physical  definition  of 
ebullition.  A  liquid  is  in  ebulli- 
tion when  it  gives  off  vapour  of 
the  same  tension  as  the  atmo- 
sphere above  it. 

The  necessity  of  this  equality 
of  tension  is  easily  explained.  If 
a  bubble  of  vapour  exists  in  the 
interior  of  a  liquid  as  at  m  (Fig. 
247),  it  is  subject  to  a  pressure 
exceeding  atmospheric  by  the 
weight  of  the  liquid  above  it.  As 
the  bubble  rises,  the  latter  ele- 
ment of  pressure  becomes  less, 
and  the  tension  of  the  vapour 
composing  the  bubble  accordingly 
diminishes,  until  it  is  reduced  to 
atmospheric  pressure  on  reaching  the  surface. 

The  boiling-point  of  a  liquid  is  therefore  necessarily  fixed,  since  it 
is  the  temperature  at  which  the  tension  of  the  vapour  at  saturation 
is  equal  to  that  of  the  atmosphere.  It  must  be  remarked,  however, 
that  this  temperature  varies  in  the  different  layers  of  the  liquid,  and 
that  it  increases  with  the  depth  below  the  surface.  Accordingly,  in 
determining  the  second  fixed  point  of  the  thermometer,  we  have 
stated  that  the  instrument  should  be  plunged  into  the 
steam,  and  not  into  the  water. 

257.  Effect  of  Pressure  upon  the  Boiling-point. — It 
evidently  follows  from  the  foregoing  considerations  that 
the  boiling-point  of  a  liquid  must  vary  with  the  pres- 
sure on  the  surface;  and  experiment  shows  that  this 
rig.  247.          is  the  case.     Water,  for  instance,  boils  at  100°  under 
the  external  pressure  of  760  millimetres;  but  if  the 
pressure  decreases,  ebullition  occurs  at  a  lower  temperature.     Under 
the  receiver  of  an  air-pump,  water  may  be  made  to  boil  at  any  tem- 


Fig.  246.— Tension  of  Vapour  during  Ebullition. 


FRANKLIN  S   EXPERIMENT. 


337 


perature  between  0°  and  100°.  In  Carry's  apparatus  (Fig.  239)  the 
water  in  the  glass  bottle  is  observed  to  enter  into  active  ebullition  a 
few  moments  before  the  appearance  of  the  ice.  The  reason,  therefore, 
why  boiling  water  has  come  to  be  associated  in  our  minds  with  a 
fixed  temperature  is  that  the  variations  of  atmospheric  pressure  are 
comparatively  small. 

At  Paris,  for  instance,  the  external  pressure  varies  between  720 
and  790  millimetres  (28'3  and  311  inches),  and  the  boiling-point, 
in  consequence,  varies  from  98'5°  to  101 '1°. 

258.  Franklin's  Experiment. — The  boiling  of  water  at  a  temperature 
lower  than  100°  may  be  shown  by  the  following  experiment: — 

A  little  water  is  boiled  in  a  flask  for  a  sufficient  time  to  expel  most 
of  the  air  contained  in  it.  The 
flask  is  then  removed  from  the 
source  of  heat,  and  is  at  the 
same  time  securely  corked.  To 
render  the  exclusion  of  air  still 
more  certain,  it  maybe  inverted 
with  the  corked  end  immersed 
in  water  which  has  been  boiled. 
Ebullition  ceases  almost  imme- 
diately; but  if  cold  water  be 
now  poured  over  the  vessel,  or, 
better  still,  if  ice  be  applied  to 
it,  the  liquid  again  begins  to 
boil,  and  continues  to  do  so  for 
a  considerable  time.  This  fact 
may  easily  be  explained:  the 
contact  of  the  cold  water  or 
the  ice  lowers  the  temperature 
and  tension  of  the  steam  which 

presses  upon  the  surface  of  the  liquid,  and  the  decrease  of  tension 
causes  the  renewal  of  ebullition. 

260.  Determination  of  Heights  by  Boiling-point. — Just  as  we  can 
determine  the  boiling-point  of  water  when  the  external  pressure  is 
given,  so,  if  the  boiling-point  be  known,  we  can  determine  the  ex- 
ternal pressure.  In  either  case  we  have  simply  to  refer  to  a  table  of 
maximum  tensions  of  aqueous  vapour  at  different  temperatures. 

As  the  barometer  is  essentially  unsuitable  for  portability,  Wollaston 
proposed  to  substitute  the  observation  of  boiling-points  as  a  means 

22 


Fig.  248. — Franklin's  Experiment. 


338 


EBULLITION. 


of  determining  pressures.  For  this  purpose  he  employed  a  thermo- 
meter with  a  large  bulb  and  with  a  scale  extending  only  a  few  de- 
grees above  and  below  100°.  He  called  this  instrument  the  barome- 
tric thermometer. 

Regnault  has  constructed  a  small  instrument  for  the  same  purpose, 
which  he  calls  the  hypsometer.  It  consists  of  a  little  boiler  heated 

by  a  spirit-lamp,  and  terminating  in  a  tele- 
scope tube  with  an  opening  at  the  side 
through  which  the  steam  escapes.  A  ther- 
mometer dips  into  the  steam,  and  projects 
through  the  top  of  the  tube  so  as  to  allow 
the  temperature  of  ebullition  to  be  read. 

This  temperature  at  once  gives  the  atmo- 
spheric pressure  by  reference  to  a  table  of 
vapour-tensions,  and  the  subsequent  com- 
putations for  determining  the  height  are  the 
same  as  when  the  barometer  is  employed 

(§  "2). 

When  only  an  approximate  result  is  de- 
sired, it  may  be  assumed  that  the  height 
above  sea-level  is  sensibly  proportional  to 
the  difference  between  the  observed  boiling- 
point  and  100°  G,  and  Soret's  formula1  may 
be  employed,  viz. : 

h =295  (ioo-0, 

where  h  is  expressed  in  metres  and  t  in 
degrees  Centigrade. 

Thus,  at  Quito,  where  the  boiling-point 
of  water  is  about  901°, the  height  above  sea- 
level  would  be  9 '9  X  295  =  2920  metres,  which  agrees  nearly  with  the 
true  height  2808  metres. 

At  Madrid,  at  the  mean  pressure,  the  boiling-point  is  97'8°,  which 
gives  2-2x295  =  649  metres;  the  actual  height  being  610  metres. 

261.  Papin's  Digester. — While  a  decrease  of  pressure  lowers  the 
boiling-point,  an  increase  of  pressure  raises  it.  Accordingly,  by  put- 
ting the  boiler  in  communication  with  a  reservoir  containing  air  at 
the  pressure  of  several  atmospheres,  we  can  raise  the  boiling-point  to 
110°,  115°,  or  120°;  a  result  often  of  great  utility  in  the  arts.  But  in 

1  If  h  be  expressed  in  feet,  and  t  in  degrees  Fahrenheit,  the  formula  becomes 
h  =  538  (212 -t). 


Fig.  250. — Hypsometer. 


PAPIN'S  DIGESTER. 


339 


order  that  the  liquid  may  actually  enter  into  ebullition,  the  space 
above  the  liquid  must  be  sufficiently  large  and  cool  to  allow  of  the 
condensation  of  the  steam.  In  a  confined  vessel,  water  may  be  raised 
to  a  higher  temperature  than  would  be  possible  in  the  open  air,  but 
it  will  not  boil.  This  is  the  case  in  the  apparatus  invented  by  the 
celebrated  Papin,  and  called  after  him  Papin's  digester.  It  is  a 
bronze  vessel  of  great  strength,  covered  with  a  lid  secured  by  a 
powerful  screw.  It  is  employed  for  raising  water  to  very  high  tem- 
peratures, and  thus  obtaining  effects  which  would  not  be  possible  with 
water  at  100°,  such  for  example  as  dissolving  the  gelatine  contained 
in  bones. 

It  is  to  be  observed  that  the  tension  of  the  steam  increases  rapidly 
with  the  temperature,  and  may  finally  acquire  an  enormous  power. 
Thus,  at  200°,  the  pressure  is  that  of  1 6  atmospheres,  that  is  about 
240  pounds  on  the  square  inch. 
In  order  to  obviate  the  risk  of 
explosion,  Papin  introduced  a 
device  for  preventing  the  pres- 
sure from  exceeding  a  definite 
limit.  This  invention  has  since 
been  applied  to  the  boilers  of 
steam-engines,  and  is  well 
known  as  the  safety-valve.  It 
consists  of  an  opening,  closed 
by  a  conical  valve  or  stopper, 
which  is  pressed  down  by  a 
lever  loaded  with  a  weight. 
Suppose  the  area  of  the  lower 
end  of  the  stopper  to  be  1 
square  inch,  and  that  the  pres- 
sure is  not  to  exceed  10  atmo- 
spheres, corresponding  to  a 
temperature  of  180°.  The 

magnitude  and  position  of  the  weight  are  so  arranged  that  the  pres- 
sure on  the  hole  is  10  times  15  pounds.  If  the  tension  of  the  steam 
exceed  1 0  atmospheres,  the  lever  will  be  raised,  the  steam  will  escape, 
and  the  pressure  will  thus  be  relieved. 

When  the  tension  of  the  steam  contained  in  the  digester  has  be- 
come considerable,  if  the  lever  be  raised,  so  as  to  permit  some  steam 
to  escape,  it  rushes  out  with  a  loud  noise,  and  produces  a  cloud  in 


Fig.  251.— Papin's  Digester. 


340  EBULLITION. 

the  air.  On  placing  the  hand  in  this  cloud,  scarcely  any  sensation 
of  heat  is  experienced,  whereas,  on  performing  the  same  experiment 
with  steam  at  the  ordinary  pressure,  the  hand  would  certainly  be 
scalded.  This  apparently  paradoxical  result  is  completely  in  accord- 
ance with  the  principles  which  have  already  been  stated  more  than 
once.  The  steam  formed  at  100°,  being  at  atmospheric  pressure,  pre- 
serves its  pressure  and  temperature  on  issuing  into  the  air.  On  the 
other  hand,  the  steam  generated  in  Papin's  digester  has  a  pressure 
greatly  exceeding  that  of  the  atmosphere,  and  accordingly  expands 
rapidly  upon  its  exit,  and  thus  performs  work  in  forcing  back  the 
external  air.  The  performance  of  this  work  is  accompanied  by  the 
loss  of  an  equivalent  quantity  of  heat,  and  the  temperature  of  the 
jet  is  consequently  considerably  lowered. 

262.  Boiling-point  of  Saline  Solutions. — When  water  holds  saline 
matters  in  solution,  the  boiling-point  rises  as  the  proportion  of  saline 
matter  in  the  water  increases.  Thus  with  sea-salt  the  boiling-point 
can  be  raised  from  100°  to  108°. 

When  the  solution  is  not  saturated,  the  boiling-point  is  not  fixed, 
but  rises  gradually  as  the  mixture  becomes  concentrated ;  but  at  a 
certain  stage  the  salt  begins  to  be  precipitated,  and  the  temperature 
then  remains  invariable.  This  is  to  be  considered  the  normal  boiling- 
point  of  the  saturated  solution.  Supersaturation,  however,  sometimes 
occurs,  the  temperature  gradually  rising  above  the  normal  boiling- 
point  without  any  deposition  of  the  salt,  until  all  at  once  precipita- 
tion begins,  and  the  thermometer  falls  several  degrees. 

The  steam  emitted  by  saline  solutions  consists  of  pure  water,  and 
it  is  frequently  asserted  to  have  the  same  temperature  as  the  steam 
of  pure  water  boiling  under  the  same  pressure;  but  the  experiments 
of  Magnus  and  others  have  shown  that  this  is  not  the  case.  Magnus, 
for  example,1  found  that  when  a  solution  of  chloride  of  calcium  was 
boiling  at  107°,  a  thermometer  in  the  steam  indicated  105|°,  and 
when  by  concentration  the  boiling-point  had  risen  to  116°,  the  ther- 
mometer in  the  steam  indicated  111 '2°. 

These  and  other  observations  seem  to  indicate  that  the  steam 
emitted  by  a  saline  solution  when  boiling,  is  in  the  condition  in  which 
the  steam  of  pure  boiling  water  would  be,  if  heated,  under  atmo- 
spheric pressure,  to  the  temperature  of  the  boiling  solution.  It  can 
therefore  be  cooled  down  to  the  boiling-point  of  pure  water  without 
undergoing  any  liquefaction.  When  cooled  to  this  point,  it  becomes 

1  PoggendorfFs  Annalcn,  cxii.  p.  415. 


DONNY'S  EXPERIMENT.  341 

saturated,  and  precisely  resembles  the  steam  of  pure  water  boiling 
under  the  same  pressure.  When  saturated  steam  loses  heat,  it  does 
not  cool,  but  undergoes  partial  liquefaction,  and  it  does  not  become 
completely  liquefied  till  it  has  lost  as  much  heat  as  would  have  cooled 
more  than  a  thousand  times  its  weight  of  superheated1  steam  one 
degree  Centigrade. 

262  A.  Boiling-point  of  Liquid  Mixtures. — A  mixture  of  two  liquids 
which  have  an  attraction  for  each  other,  and  will  dissolve  each  other 
freety  in  all  proportions — for  example,  water  and  alcohol — has  a  boil- 
ing-point intermediate  between  those  of  its  constituents.  But  a 
mechanical  mixture  of  two  liquids  between  which  no  solvent  action 
takes  place — for  example,  water  and  sulphide  of  carbon — has  a  boiling- 
point  lower  than  either  of  its  constituents.  If  steam  of  water  is 
passed  into  liquid  sulphide  of  carbon,  or  if  sulphide  of  carbon  vapour 
is  passed  into  water,  a  mixture  is  obtained  which  boils  at  42 '6°  G, 
being  four  degrees  lower  than  the  boiling-point  of  sulphide  of  carbon 
alone.  This  apparent  anomaly  is  a  direct  consequence  of  the  laws  of 
vapours  stated  in  §  244 ;  for  the  boiling-point  of  such  a  mixture  is  the 
temperature  at  which  the  sum  of  the  vapour-tensions  of  the  two 
independent  ingredients  is  equal  to  one  atmosphere. 

263.  Influence  of  Dissolved  Air  upon  the  Eoiling-point. — The 
presence  of  air  in  the  midst  of  the  liquid  ^nass  ?;s  u  necessary 
condition  of  regularity  of  ebullition,  and  of  its  production  at  the 
normal  temperature;  this  is  shown  by  several  convincing  experi- 
ments. 

1.  Donnys  Experiment — We  take  a  glass  tube  bent  twice,  and 
terminated  at  one  of  its  extremities  by  a  series  of  bulbs.  The  first 
step  is  to  wash  it  carefully  with  alcohol  and  ether,  finally  leaving  in 
it  some  diluted  sulphuric  acid.  These  operations  are  for  the  purpose 
of  removing  the  solid  particles  adhering  to  the  sides,  which  always 
detain  portions  of  air.  Water  is  then  introduced  and  boiled  long 
enough  to  expel  the  air  dissolved  in  it,  and  while  ebullition  is  pro- 
ceeding, the  end  of  the  apparatus  is  hermetically  sealed.  The  other 
extremity  is  now  plunged  in  a  strong  solution  of  chloride  of  calcium, 
which  has  a  very  high  boiling-point,  and  the  tube  is  so  placed  that 
all  the  water  shall  lie  in  this  extremity;  it  will  then  be  found  that 
the  temperature  may  be  raised  to  135°  without  producing  ebullition. 

1  That  is  steam  heated  above  the  temperature  of  saturation.  Philosophically  speaking, 
superheated  steam  is  merely  nonsaturated  steam;  but  the  name  is  never  used  except  where 
the  temperature  exceeds  the  atmospheric  boiling-point. 


342 


EBULLITION. 


At  about  tins  temperature  bubbles  of  steam  are  seen  to  be  formed, 
and  the  entire  liquid  mass  is  thrown  forward  with  great  violence. 


Fig.  252 — Donny's  Experiment. 

The  bulbs  at  the  end  of  the  tube  are  intended  to  diminish  the  shock 
thus  produced. 

2.  Dufours  Experiment — This  experiment  is  still  more  decisive. 
Ajnixtureto£Jins_eed-oil  and  oil  of  cloves,  whose  respective  densities 
art^  about  ,*9S  and  1U0  J .,  is  so  prepared  that,  for  temperatures  near  1 00°, 
the  density' of ;  the  ^whoie  is  nearly  that  of  water.  This  mixture  is 
pkced  irra  cubical  box:  of  sheet-iron,  with  two  holes  opposite  each 
other,  which  are  filled  with  glass,  so  as  to  enable  the  observer  to 
perceive  what  is  passing  within.  The  box  is  placed  in  a  metallic 
envelope,  which  permits  of  its  being  heated  laterally.  When  the 
temperature  of  1 20°  has  been  reached,  a  large  drop  of  water  is  allowed 
to  fall  into  the  mixture,  which,  on  reaching  the  bottom  of  the  box, 
is  partially  converted  into  vapour,  and  breaks  up  into  a  number  of 
smaller  drops,  some  of  which  take  up  a  position  between  the  two 
windows,  so  as  to  be  visible  to  the  observer.  The  temperature  may 
now  be  raised  to  140°,  150°,  or  even  180°,  without  producing  evapora- 
tion of  any  of  these  drops.  Now  the  maximum  tension  of  steam  at 
180°  is  equal  to  10  atmospheres,  and  yet  we  have  the  remarkable 
phenomenon  of  a  drop  of  water  remaining  liquid  at  this  temperature 
under  no  other  pressure  than  that  of  the  external  air  increased  by  an 
inch  or  two  of  oil.  The  reason  is  that  the  air  necessary  to  evapora- 
tion is  not  supplied.  If  the  drops  be  touched  with  a  rod  of  metal, 
or,  better  still,  of  wood,  they  are  immediately  converted  into  vapour 


DUFOUR'S  EXPERIMENT.  343 

with  great  violence,  accompanied  by  a  peculiar  noise.  This  is 
explained  by  the  fact  that  the  rods  used  always  carry  a  certain 
quantity  of  condensed  air  upon  their  surface,  and  by  means  of  this 
air  the  evaporation  is  produced.  The  truth  of  this  explanation  is 
proved  by  the  fact,  that  when  the  rods  have  been  used  a  certain 
number  of  times,  they  lose  their  power  of  provoking  ebullition,  owing, 
no  doubt,  to  the  exhaustion  of  the  air  which  was  adhering  to  their 
surfaces. 

3.  Production  of  Ebullition  by  the  formation  of  Bubbles  of  Gas 
in  the  'midst  of  a  Liquid. — A  retort  is  carefully  washed  with 
sulphuric  acid,  and  then  charged  with  water  slightly  acidulated,  from 
which  the  air  has  been  expelled  by  repeated  boiling.  The  retort 
communicates  with  a  manometer  and  with  an  air-pump.  The  air  is 
exhausted  until  a  pressure  of  only  150  millimetres  is  attained,  corre- 
sponding to  GO0  as  boiling-point.  Dufour  has  shown  that  under 
these  conditions  the  temperature  may  be  gradually  raised  to  75° 
without  producing  ebullition.  But  if,  while  things  are  in  this  con- 
dition, a  current  of  electricity  is  sent  through  the  liquid  by  means  of 
two  platinum  wires  previously  immersed  in  it,  the  bubbles  of  oxygen 
and  hydrogen  which  are  evolved  at  the  wires  immediately  produce 
violent  ebullition,  and  a  portion  of  the  liquid  is  projected  explosively, 
as  in  Doriny's  experiment. 

From  these  experiments  we  may  conclude  that  liquid,  when  not 
in  contact  with  gas,  has  a  difficulty  in  making  a  beginning  of  vapor- 
ization, and  may  hence  remain  in  the  liquid  state  even  at  tempera- 
tures at  which  vaporization  would  upon  the  whole  involve  a  fall  of 
potential  energy. 

That  vapour  (as  well  as  air)  can  furnish  the  means  of  overcoming 
this  difficulty,  is  established  by  the  fact  noted  by  Professor  G.  C. 
Foster,1  that  when  a  liquid  has  been  boiling  for  some  time  in  a  retort, 
it  sometimes  ceases  to  exhibit  the  movements  characteristic  of  ebulli- 
tion, although  the  amount  of  vapour  evolved  at  the  surface,  as  mea- 
sured by  the  amount  of  liquid  condensed  in  the  receiver,  continues 
undirninished.  In  these  circumstances,  it  would  appear  that  the 
superficial  layer  of  liquid,  which  is  in  contact  with  its  own  vapour, 
is  the  only  part  that  is  free  to  vaporize. 

The  preceding  remarks  explain  the  reluctance  of  water  to  boil  in 
glass  vessels  carefully  washed,  and  the  peculiar  formation,  in  these 
circumstances,  of  large  bubbles  of  steam,  causing  what  is  called  boil- 

1  Watts's  Dictionary  of  Chemistry,  art.  "Heat,"  p.  88. 


344 


EBULLITION. 


ing  by  bumping.  In  the  case  of  sulphuric  acid,  the  phenomenon  is 
much  more  marked;  if  this  liquid  be  boiled  in  a  glass  vessel,  enormous 
bubbles  are  formed  at  the  sides,  which,  on  account  of  the  viscous 

nature  of  the  liquid,  raise 
the  mass  of  the  liquid 
above  them,  and  then  let 
it  fall  back  with  such 
violence  as  sometimes  to 
break  the  vessel.  This 
inconvenience  may  be 
Fig.  253.— Apparatus  for  boiling  Sulphuric  Acid.  avoided  by  using  an  an- 

nular  brazier  (Fig.  253), 
by  means  of  which  the  upper  part  only  of  the  liquid  is  heated. 

The  ebullition  of  ether  and  alcohol  presents  some  similar  features, 
probably  because  these  liquids  dissolve  the  fatty  particles  on  the 
surface  of  the  glass,  and  thus  adhere  to  the  sides  very  strongly. 
v  264.  Spheroidal  State. — This  is  the  name  given  to  a  peculiar  con- 
dition which  is  assumed  by  liquids  when  exposed  to  the  action  of 
very  hot  metals. 

If  we  take  a  smooth  plate  of  iron  or  silver,  and  let  fall  a  drop  of 
water  upon  it,  the  drop  will  evaporate  more  rapidly  as  the  tempera- 
ture of  the  plate  is  increased  up 
to  a  certain  point.  When  the 
temperature  of  the  plate  exceeds 
this  limit,  which,  for  water,  ap- 
pears to  be  about  J  50°,  the  drop 
assumes  a  spheroidal  form,  rolls 
about  like  a  ball  or  spins  on  its 
axis,  and  frequently  exhibits  a 
beautiful  rippling,  as  represented 
in  the  figure.  While  in  this  con- 

O 

dition,  it  evaporates  much  more 
slowly  than  when  the  plate  was 
at  a  lower  temperature.      This 
latter  circumstance  is  important, 
and  is  easily  verified  by  experi- 
ment.    If  the  plate  be  allowed  to  cool,  a  moment  arrives  when  the 
globule  of  water  flattens  out,  and  boils  rapidly  away  with  a  hissing 
noise. 

These  phenomena  have  been  long  known,  and  were  studied  by 


Fig.  254.— Globule  in  the  Spheroidal  State. 


THE   SPHEROIDAL   STATE.  345 

Leidenfrost  and  Klaproth;  but  the  subject  has  recently  been  more 
completely  investigated  by  Boutigny.  All  liquids  are  probably  capable 
of  assuming  the  spheroidal  state;  Among  those  which  have  been 
tested  are  alcohol,  ether,  liquid  sulphurous  acid,  and  liquid  nitrous 
oxide.  When  in  this  state  they  do  not  boil.  Sometimes  bubbles  of 
steam  are  seen  to  rise  and  burst  at  the  top  of  the  globule,  but  these 
are  always  owing  to  some  roughness  of  the  surface,  which  prevents 
the  steam  from  escaping  in  any  other  way;  when  the  surface  is  smooth, 
no  bubbles  are  observed. 

If  the  temperature  of  the  liquid  be  measured  by  means  of  a  ther- 
mometer with  a  very  small  bulb,  or  a  thermo-electric  junction,  it  is 
always  found  to  be  below  the  boiling-point. 

265.  Freezing  of  Water  and  Mercury  by  means  of  the  Spheroidal 
utate. — This  latter  property  enables  us  to  obtain  some  very  striking 
and  paradoxical  results.     The  boiling-point  of  liquid  sulphurous  acid 
is  — 10°C.,  and  that  of  liquid  nitrous  oxide  is  about  — 70°  C.     If  a 
silver  or  platinum  crucible  be  heated  to  redness  by  a  powerful  lamp, 
and  some  liquid  sulphurous  acid  be  then  poured  into  it,  this  latter 
assumes  the  spheroidal  state ;  and  drops  of  water  let  fall  upon  it  are 
immediately  frozen.     Mercury  can  in  like  manner  be  frozen  in  a  red- 
hot  crucible  by  employing  liquid  nitrous  oxide  in  the  spheroidal 
state. 

These  experiments  are  due  to  Boutigny,  who  called  attention  to 
them  as  remarkable  exceptions  to  the  usual  tendency  of  bodies  to 
equilibrium  of  temperature.  The  exception  is  of  the  same  kind  as 
that  presented  by  a  vessel  of  water  boiling  at  a  constant  temperature 
of  100°  over  a  hot  fire,  the  heat  received  by  the  liquid  being  in  both 
cases  expended  in  producing  evaporation. 

266.  The  Metal  not  in  Contact  with  the  Liquid.— The  basis  of  the 
entire  theory  of  liquids  in  the  spheroidal  state  is  the  fact  that  the 
liquid  and  the  metal  plate  do  not  come  into  contact.     This  fact  can 
be  proved  by  direct  observation. 

The  plate  used  must  be  quite  smooth  and  accurately  levelled. 
When  the  plate  is  heated,  a  little  water  is  poured  upon  it,  and 
assumes  the  spheroidal  state.  By  means  of  a  fine  platinum  wire 
which  passes  into  the  globule,  the  liquid  is  kept  at  the  centre  of  the 
metal  plate.  It  is  then  very  easy,  by  placing  a  light  behind  the 
globule,  to  see  distinctly  the  space  between  the  liquid  and  the  plate. 
The  appearance  thus  presented  may  be  easily  thrown  on  a  screen  by 
means  of  the  electric  light. 


346 


EBULLITION. 


The  interruption,  of  contact  can  also  be  proved  by  connecting 
(through  a  galvanometer)  one  pole  of  a  battery  with  the  hot  plate, 
vhile  a  wire  from  the  other  pole  is  dipped  in  the  liquid.  The  cur- 


Fig.  255.— Separation  between  Globule  and  Plate. 

rent  refuses  to  circulate  if  the  liquid  is  in  the  spheroidal  state,  but  is 
immediately  established  when,  on  cooling  the  plate,  the  liquid  begins 
to  boil. 

This  separation  is  maintained  by  the  rush  of  steam  from  the  under- 
surface  of  the  globule,  which  is  also  the  cause  of  the  peculiar  move- 
ments above  described. 

In  consequence  of  the  separation,  heat  can  only  pass  to  the  globule 
by  radiation,  and  hence  its  comparatively  low  temperature  is  ac- 
counted for. 

The  absence  of  contact  between  a  liquid  and  a  metal  at  a  high 
temperature  may  be  shown  by  several  experiments.  If,  for  instance, 
a  ball  of  platinum  be  heated  to  bright  redness,  and  plunged  (Fig.  256) 
into  water,  the  liquid  is  seen  to  recede  on  all  sides,  leaving  an  envelope 
of  vapour  round  the  ball.  This  latter  remains  red  for  several  seconds, 
and  contact  does  not  take  place  till  its  temperature  has 
fallen  to  about  150°.  An  active  ebullition  then  takes 
place,  and  an  abundance  of  steam  is  evolved. 

If  drops  of  melted  sugar  be  let  fall  on  water,  they  will 
float  for  a  short  time,  though  their  density  is  greater 
than  that  of  water  (§  79),  contact  being  prevented  by 
their  high  temperature.     A  similar  phenomenon  is  ob- 
served when  a  fragment  of  potassium  is  thrown  on  water. 
1"ne  wa^er  is  decomposed ;   its  hydrogen  takes  fire  and 
burns  with  a  red  flame ;  its  oxygen  combines  with  the 
potassium  to  form  potash ;  and  the  globule  of  potash  floats  upon  the 
surface  without  touching  it,  owing  to  the  high   temperature  under 


DISTILLATION. 


347 


which  it  is  formed.  After  a  few  seconds  the  globule  cools  sufficiently 
to  come  into  contact  with  the  water,  and  bursts  with  a  slight  noise. 

267.  Distillation. — Distillation  consists  in  boiling  a  liquid  and 
condensing  the  vapour  evolved.  It  enables  us  to  separate  a  liquid 
from  the  solid  matter  dissolved  in  it,  and  to  effect  a  partial  separa- 
tion of  the  more  volatile  constituent  of  a  mixture  from  the  less 
volatile. 

The  apparatus  employed  for  this  purpose  is  called  a  still.  One  of 
the  simpler  forms,  suitable  for  distilling  water,  is  shown  in  Fig.  257. 

It  consists  of  a  retort  a,  the  neck  of  which  c  communicates  with  a 


Fig.  257.— Still. 

spiral  tube  dd  called  the  worm,  placed  in  the  vessel  e,  which  contains 
cold  water.  The  water  in  the  retort  is  raised  to  ebullition,  the  steam 
given  off  is  condensed  in  the  worm,  and  the  distilled  water  is  col- 
lected in  the  vessel  g. 

As  the  condensation  of  the  steam  proceeds,  the  water  of  the  cooler 
becomes  heated,  and  must  be  renewed  ;  for  this  purpose  a  tube 
descending  to  the  bottom  of  the  cooler  is  supplied  with  a  continuous 
stream  of  cold  water  from  above,  while  the  superfluous  water  flows 
out  by  the  tube  i  at  the  upper  part  of  the  cooler.  In  this  way  the 
warm  water,  which  rises  to  the  top,  is  continually  removed.  The 
boiler  is  filled  about  three-quarters  full,  and  the  water  in  it  can  from 
time  to  time  be  renewed  by  the  opening/;  but  it  is  advisable  not  to 
carry  the  process  of  distillation  too  far,  and  to  throw  away  the  liquid 


348  EBULLITION. 

remaining  in  the  boiler  when  its  volume  has  been  reduced  to  a  fourth 
or  a  fifth  of  what  it  was  originally.  By  exceeding  this  limit  we  run 
the  risk  of  impairing  the  purity  of  the  water  by  the  carrying  over 
of  some  of  the  solid  matter  contained  in  the  liquid  in  the  boiler. 

289.  Circumstances  which  Influence  Rapidity  of  Evaporation. — In 
the  case  of  a  liquid  exposed  to  the  air,  and  at  atmospheric  tempera- 
ture, the  rapidity  of  evaporation  increases  with  the  extent  of  free 
surface,  the  dryness  of  the  air,  and  the  rapidity  of  renewal  of  the 
air  immediately  above  the  surface. 

In  the  case  of  a  liquid  evaporated  by  boiling,  the  quantity  evapo- 
rated in  a  given  time  is  proportional  to  the  heat  received.  This 
depends  upon  the  intensity  of  the  source  of  heat,  the  facility  with 
which  heat  passes  through  the  sides  of  the  vessel,  and  the  area  of 
heating  surface,  that  is  to  say,  of  surface  (or  more  properly  lamina) 
which  is  in  contact  with  the  liquid  on  one  side,  and  with  the  source 
of  heat  on  the  other. 


CHAPTER    XXVII 


MEASUREMENT   OF  THE  MAXIMUM  TENSIONS  OF  VAPOURS. 


270.  Tension  of  Aqueous  Vapour. — The  knowledge  of  the  maximum 
tension  of  the  vapour  of  water  at  various  temperatures  is  important, 
not  only  from  a  theoretical,  but  also  from  a  practical  point  of  view, 
inasmuch  as  this  tension  is  the  motive  force  in  the  steam-engine. 
Experiments   for  the  purpose  of  determining   the   values  of  this 
element  have  accordingly  been  undertaken  by  several  experimenters 
in  different  countries.     The  researches  conducted  by  Regnault  are 
especially  remarkable  for  the  range  of  temperature  which  they  em- 
brace, as  well  as  for  the  number  of  observations  which  they  include, 
and  the  extreme  precision  of  the  methods  employed.     Next  to  these 
in  importance  are  the  experiments  of  Magnus  in  Germany  and  of 
Fairbairn  and  Tate  in  England. 

271.  Dalton's  Apparatus. — The  first  investigations  in  this  subject 
which  have  any  pretensions  to  accuracy  were  those  of  Dalton.     The 
apparatus  which  he  employed  is  represented  in  Fig.  259.     Two  baro- 
metric tubes  A  and  B  are  inverted  in  the  same  cistern  H ;  one  is  an 
ordinary  barometer,  the  other  a  vapour-barometer;  that  is,  a  baro- 
meter in  which  a  few  drops  of  water  have  been  passed  up  through 
the  mercury.     The  two  tubes,  attached  to  the  support  CD,  are  sur- 
rounded by  a  cylindrical  glass  vessel  containing  water  which  can  be 
raised  to  different  temperatures  by  means  of  a  fire.     The  first  step 
is  to  fill  the  vessel  with  ice,  arid  then  read  the  difference  of  level  of 
the  mercury  in  the  two  tubes.     This  can  be  done  by  separating  the 
fragments  of  ice.     The  difference   thus  observed  is  the  tension  of 
aqueous  vapour  at  zero  Centigrade.      The  ice  is  then  replaced  by 
water,  and  the  action  of  the  fire  is  so  regulated  as  to  give  different 
temperatures,  ranging  between  0°  and  100° C.,  each  of  which  is  pre- 
served constant  for  a  few  minutes,  the  water  being  at  the  same  time 


350 


MEASUREMENT  OF  THE 


well  stirred  by  means  of  the  agitator  pq,  so  as  to  insure  uniformity 
of  temperature  throughout  the  whole  mass.     The  difference  of  level 

in  the  two  barometers  is  read  off  in  each 
case ;  and  we  have  thus  the  means  of 
constructing,  with  the  aid  of  graphical 
or  numerical  interpolation,  a  complete 
table  of  vapour- tensions  from  0°  to  100° 
C.  At  or  about  this  latter  temperature 
the  mercury  in  the  vapour-barometer 
falls  to  the  level  of  the  cistern ;  and  the 
method  is  therefore  inapplicable  for 
higher  temperatures.  Such  a  table  was 
constructed  by  Dalton. 

272.  Regnault's  Modifications. — Dai- 
ton's  method  has  several  defects.  In 
the  first  place,  it  is  impossible  to  insure 
that  the  temperature  shall  be  every- 
where the  same  in  a  column  as  long  as 
that  which  is  formed  by  the  vapour  at 
70°,  75°,  and  higher  temperatures.  In 
the  second  place,  there  is  always  a  good 
deal  of  uncertainty  in  observing  the 
difference  of  level  through  the  sides  of 
the  cylindrical  glass  vessel.  Regnault 
employed  this  method  only  up  to  the 
temperature  of  50°  C.  At  this  tempera- 
ture the  tension  of  the  vapour  is  only 

about  9  centimetres  (less  than  4  inches)  of  mercury,  and  it  is  thus 
unnecessary  to  heat  the  barometers  throughout  their  entire  length. 
The  improved  apparatus  is  represented  in  Fig.  260.  The  two  baro- 
metric tubes,  of  an  interior  diameter  of  1 4  millimetres,  traverse  two 
holes  in  the  bottom  of  a  metal  box.  In  one  of  the  sides  of  the  box 
is  a  large  opening  closed  with  plate-glass,  through  which  the  necessary 
observations  can  be  made  with  great  accuracy.  On  account  of  the 
shortness  of  the  liquid  column  it  was  very  easy,  by  bringing  a  spirit- 
lamp  within  different  distances  of  the  box,  to  maintain  for  a  suffi- 
cient time  any  temperature  between  0°  arid  50°  C. 

The  difference  of  level  between  the  two  mercurial  columns  should 
be  reduced  to  0°  C.  by  the  ordinary  correction.  We  should  also  take 
into  consideration  the  short  column  of  water  which  is  above  the 


Fig.  259. — Dalton's  Apparatus, 


MAXIMUM   TENSIONS   OF   VAPOURS. 


351 


mercury  in  the  vapour  barometer,  and  which,  by  its  weight,  produces 
a  depression  that  may  evidently  be  expressed  in  mercury  by  dividing 
the  height  of  the  column  by  13'59. 

To  adapt  this  apparatus  to  low 
temperatures,  it  is  modified  in  the 
following  way.  The  upper  ex- 
tremity of  the  vapour  barometer 
tube  is  drawn  out  and  connected 
with  a  small  copper  tube  of  three 
branches,  one  of  which  communi- 
cates with  an  air-pump,  and  an- 
other with  a  glass  globe  of  the 
capacity  of  about  500  cubic  centi- 
metres. In  the  interior  of  this 
globe  is  a  small  bulb  of  thin  glass 
containing  water,  from  which  all 
the  air  has  been  expelled  by  boil- 
ing. The  globe  is  several  times 
exhausted  of  air,  and  after  each  ex- 
haustion is  refilled  with  air  which 
has  been  passed  over  desiccating 
substances.  After  the  last  exhaus- 
tion, the  tube  which  establishes 
communication  with  the  air-pump 
is  hermetically  sealed,  the  box  is 
filled  with  ice,  and  the  tension  at 
zero  of  the  dry  air  left  behind  in 
the  globe  by  the  air-pump  is  mea- 
sured ;  it  is  of  course  exceedingly 

small.  Heat  is  then  applied  to  the  globe,  the  little  bulb  bursts,  and 
the  globe,  together  with  the  space  above  the  mercury,  is  filled  with 
vapour.  This  form  of  apparatus  can  also  be  employed  to  measure 
tensions  at  temperatures  up  to  50°,  the  only  difference  being  that  the 
ice  is  replaced  by  water  at  different  temperatures,  allowance  being 
made,  in  each  case,  for  the  elastic  force  of  the  unexhausted  air. 

In  the  case  of  temperatures  below  zero,  the  box  is  no  longer 
required,  and  the  globe  alone  is  placed  in  a  vessel  containing  a  freez- 
ing mixture.  The  barometric  tubes  are  surrounded  by  the  air  of  the 
apartment. 

In  this  case  the  space  occupied  by  the  vapour  is  at  two  different 


Fig.  2GO. — Modified  Form  of  Dalton's  Apparatus. 


352  MEASUREMENT   OF   THE 

temperatures  in  different  parts,  but  it  is  evident  that  equilibrium 
can  exist  only  when  the  tension  is  the  same  throughout.  But  the 
tension  of  the  vapour  in  the  globe  can  never  exceed  the  maximum 
tension  for  the  actual  temperature ;  this  must  therefore  be  the  tension 
throughout  the  entire  space,  and  is  consequently  that  which  corre- 
sponds to  the  difference  of  level  observed. 

In  reality  what  happens  is  as  follows: — The  low  temperature  of 
the  globe  causes  some  of  the  vapour  to  condense;  equilibrium  is 
consequently  destroyed,  a  fresh  quantity  of  vapour  is  produced,  enters 
the  globe,  arid  is  there  condensed,  and  so  on,  until  the  tension  is 
everywhere  the  same  as  the  maximum  tension  due  to  the  tempera- 
ture of  the  globe.  This  condensation  of  vapour  in  the  cold  part  of 
the  space  was  utilized  by  Watt  in  the  steam-engine;  it  is  i\\Q prin- 
ciple of  ike  condenser. 

Before  Regnault,  Gay-Lussac  had  already  turned  this  principle  to 
account  in  a  similar  manner  for  the  measurement  of  low  tempera- 
tures. 

By  using  chloride  of  calcium  mixed  with  successively  increasing 
quantities  of  snow  or  ice,  the  temperature  can  be  brought  as  low  as 
— 32° C.  (— 25'6°  F.),  and  it  can  be  shown  that  the  tension  of  the  vapour 
of  water  is  quite  appreciable  even  at  this  point. 

273.  Measurement  of  Maximum  Tensions  for  Temperatures  above  50°. 
— In  investigating  the  tension  of  the  vapour  of  water  at  temperatures 
above  50°,  Regnault  made  use  of  the  fact  that  the  maximum  tension 
of  steam  at  the  boiling-point  is  equal  to  the  external  pressure. 

His  apparatus  consists  (Fig.  26  J)  of  a  copper  boiler  containing 
water  which  can  be  raised  to  different  temperatures  indicated  by 
very  delicate  thermometers.  The  vapour  produced  passes  through  a 
tube  inclined  upwards,  which  is  kept  cool  by  a  constant  current  of 
water ;  in  this  way  the  experiment  can  be  continued  for  any  length 
of  time,  as  the  vapour  formed  by  ebullition  is  condensed  in  the  tube, 
and  flows  back  into  the  boiler.  The  tube  leads  to  the  lower  part  of 
a  large  reservoir,  in  which  the  air  can  be  either  rarefied  or  com- 
pressed at  will.  This  reservoir  is  in  communication  with  a  mano- 
meter. The  apparatus  shown  in  the  figure  is  that  employed  for 
pressures  not  exceeding  5  atmospheres.  Much  greater  pressures, 
extending  to  28  atmospheres,  can  be  attained  by  simply  altering  the 
dimensions  of  the  apparatus  without  any  change  in  its  principle. 
The  manometer  employed  in  this  case  was  the  same  as  that  used  in 
testing  Boyle's  law,  consisting  of  a  long  column  of  mercury  (§  121). 


MAXIMUM  TENSIONS   OF   VAPOURS. 


In  using  this  apparatus,  the  air  in  the  reservoir  is  first  rarefied 
until  the  water  boils  at  about  50°  C. ;  the  occurrence  of  ebullition 
being  recognized  by  its  characteristic  sound,  and  by  the  temperature 


Fig.  2G1. — Regnault's  Apparatus  for  High  Temperatures. 

remaining  invariable.  This  steadiness  of  temperature  is  of  great 
advantage  in  making  the  observations,  inasmuch  as  it  enables  the 
thermometers  to  come  into  perfect  equilibrium  of  temperature  with 
the  water.  The  tension  indicated  by  the  manometer  during  ebulli- 
tion is  exactly  that  of  the  vapour  produced.  By  admitting  air  into 
the  reservoir,  the  boiling-point  is  raised  by  successive  steps  until  it 
reaches  100°.  After  this,  air  must  be  forced  into  the  reservoir  by  a 
compression-pu  mp. 

The  following  is  an  abstract  of  the  results  thus  obtained: — 


Temperatures 
Centigrade. 

-  32°         .      . 

Tensions  in 
Millimetres  of 
Mercury. 

.      .              0-32 

Temperatures 
Centigrade. 

5°       .     .     . 

Tensions  in 
Millimetres  of 
Mercurj. 

.      .        6-53 

-20    . 

0'93 

10    .     .     .     . 

.     .     .       9-17 

-10 

2'09 

15    .     .     .     . 

.     .     .     1270 

-   5 

3-11 

20    .          .     . 

.     .     .     17-39 

0 

4'60 

2$         .     .     . 

.     .     .     23-53 

23 

354 


MEASUREMENT   OF   THE 


Temperatures 
Centigrade. 


Tensions  in 

Millimetres  of 

Mercury. 

30° 31-55 

35  ..          ....  41-82 

40 54-91 

45 71-39 

50 91-98 

55 117-47 

60 148-70 

65 186-94 

Tensions  in 
Atmospheres. 

100° 1 

121 2-025 

134 3:008 

144 4-000 

152 4-971 

159 5-966 

171  .  .  8-036 


70° 233-09 

75 288-51 

80 354-64 

85 433-04 

90 525-45 

95 633-77 

100  .            .  760-00 


Tensions  in 
Atmospheres. 

180° 9-929 

189  .......  12-125 

199 15-062 

213 19-997 

225 25-125 

239  .            ,  27-534 


274.  Curves  of  Vapour-tension. — The  comparison  of  these  tensions 
with  their  corresponding  temperatures  affords  no  clue  to  any  simple 
relation  between  them  which  might  be  taken  as  the  physical  law  of 
the  phenomena.  It  would  appear  that  the  law  of  variation  of 
maximum  tensions  is  incapable  of  being  thrown  into  any  simple 
expression— judging  at  least  from  the  failure  of  all  efforts  hitherto 
made.  An  attentive  examination  of  the  above  table  will  enable  us 
to  assert  only  that  the  maximum  tension  varies  very  rapidly  with 

the  temperature.  Thus  be- 
tween 0°  and  100°  the  variation 
is  only  1  atmosphere,  but  be- 
tween 100°  and  200°  it  is  about 
15,  and  between  200°  and  230° 
about  13  atmospheres. 

The  clearest  way  of  repre- 
senting to  the  mind  the  law  ac- 
cording to  which  vapour-ten- 
sion varies  with  temperature,  is 
by  means  of  a  curve  whose  or- 
dinates   represent  vapour-ten- 
sions, while  the  abscissae  repre- 
sent  the    corresponding    tem- 
peratures.    Such  a  curve  is  exhibited  in  Fig.  262.     Lengths  propor- 
tional to  the  temperatures,  reckoned  from  0°  G,  are  laid  off  on  the 
base-line  (called  the  line  of  abscissae),  and  perpendiculars  (called  ordi- 


Fig.  262. 


MAXIMUM  TENSIONS  OF  VAPOURS.  355 

nates)  are  erected  at  their  extremities,  the  lengths  of  these  perpendi- 
culars being  made  proportional  to  the  vapour-tensions.  The  scales 
employed  for  the  two  sets  of  lengths  are  of  course  quite  independent 
of  one  another,  their  selection  being  merely  a  question  of  convenience. 
The  curve  itself  is  obtained  by  joining  the  extremities  of  the  per- 
pendiculars, taking  care  to  avoid  sudden  changes  of  direction ;  and 
it  not  only  serves  to  convey  to  the  mind  an  idea  of  the  amounts  of 
vapour- tensions  and  their  rates  of  variation  at  different  tempera- 
tures, but  also  furnishes  the  readiest  means  of  determining  the 
vapour -tensions  at  temperatures  intermediate  between  those  of 
observation  (see  §88B). 

It  will  be  noticed  that  the  curve  becomes  steeper  as  the  tempera- 
ture increases,  indicating  that  the  tension  increases  faster  than  the 
temperature. 

275.  Empirical  Formulas. — Though  all  attempts  at  finding  a  rational 
formula  for  vapour-tension  in  terms  of  temperature  have  hitherto   f 
failed,  it  is  easy  to  devise  empirical  formulae  which  yield  tolerably        i*      * 
accurate  results  within  a  limited  range  of  temperature;  and  by      \ 
altering  the  values  of  the  constants  in  such  a  formula  by  successive    * 
steps,  it  may  be  adapted  to  represent  in  succession  the  different  por- 
tions of  the  curve  above  described. 

The  simplest  of  these  approximate  formulae1  is  that  of  Dulong  and 
Arago,  which  may  be  written — 


(-rlr)     or 

and  gives  the  maximum  tension  in  atmospheres,  corresponding  to 
the  temperature  C°  Centigrade,  or  F°  Fahrenheit.  This  formula  is 
rigorously  correct  at  100°  C.,  and  gives  increasing  errors  as  the  tem- 
perature departs  further  from  this  centre,  the  errors  amounting  to 
about  1J  per  cent,  at  the  temperatures  80°  C.  and  225°  C.  Hence  it 
appears  that  between  these  limits  the  maximum  tension  of  aqueous 
vapour  is  nearly  proportional  to  the  fifth  power  of  the  excess  of  the 
temperature  above  —  40°  C. 

276.  Tensions  of  the  Vapours  of  Different  Liquids. — Dalton  held  that 
the  vapours  of  different  liquids  have  equal  tensions  at  temperatures 
equally  removed  from  their  boiling-points.  Thus  the  boiling-point 
of  alcohol  being  78°,  the  tension  of  alcohol  vapour  at  70°  should  be 
equal  to  that  of  the  vapour  of  water  at  92°.  If  this  law  were  correct, 

1  For  a  more  accurate  formula,  see  Rarikine  on  Steam-engine,  p.  237. 


356  MEASUREMENT   OF   THE 

it  would  only  be  necessary  to  know  the  boiling-point  of  any  liquid  in 
order  to  estimate  the  tension  of  its  vapour  at  any  given  temperature; 
but  subsequent  experiment  has  shown  that  the  law  is  far  from  being 
rigorously  exact,  though  it  is  approximately  correct  for  temperatures 
differing  by  only  a  few  degrees  from  the  boiling-points. 

Regnault  has  performed  numerous  experiments  on  the  vapour- 
tensions  of  some  of  the  more  volatile  liquids,  employing  for  this 
purpose  the  same  form  of  apparatus  which  had  served  for  deter- 
mining the  tensions  of  aqueous  vapour.  The  following  are  some  of 
his  results : — 

VAPOUR  OF  ALCOHOL. 


Temperatures  Tensions  in 

Centigrade.  Millimetres. 

-20° 3-24 

0  1270 


+  10 24-23 


Temperatures  Tensions  in 

Centigrade.  Millimetres. 

+  30° 78-52 

100  .          .  1697-55 


155 6259-19 


VAPOUR  OF  ETHER. 


-20° 68-90 

0 184-39 

+  10   .          .  280-83 


+  30° 634-80 

100 4953-30 

120  .          .  7719-20 


VAPOUR  OF  SULPHIDE  OF  CARBON. 


-20° 47-30 

0 127-91 

+  10  .  198-46 


+  30° 434-62 

100 3325-15 

150  .          .  9095-94 


>  277.  Expression  of  Vapour-tension  in  Absolute  Measure. — The 
maximum  tension  of  a  given  vapour  at  a  given  temperature  is,  from 
its  very  nature,  independent  of  geographical  position,  and  should 
therefore,  properly  speaking,  be  denoted  by  one  and  the  same  number 
at  all  places.  This  numerical  uniformity  will  not  exist  if  the  tension 
be  expressed,  as  in  the  preceding  sections,  in  terms  of  the  length  of 
a  column  of  mercury  which  balances  it.  For  example,  in  order  to 
adapt  Regnault's  determinations  to  London,  we  must  multiply  them 
by  the  fraction  -f  Jf-J-,  inasmuch  as  3456  millimetres  of  mercury  exert 
the  same  pressure  at  London  as  3457  at  Paris.  In  general,  to  adapt 
determinations  of  pressure  made  at  a  place  A,  to  another  place  B,  we 
must  multiply  them  by  the  fraction 

gravity  at  A 
gravity  at  B' 

If  the  length  of  mercurial  column  at  0°C.  which  balances  a  vapour- 
tension  at  a  given  place  be  multiplied  by  the  value  of  g  (denoting 
intensity  of  gravity)  at  that  place,  the  product  may  be  called  the 


MAXIMUM  TENSIONS  OF  VAPOURS.  35? 

absolute  value  of  the  vapour- tension  ;  for  the  products  thus  obtained 
will  be  the  same  at  all  localities.  This  is  the  proper  mode  of  treat- 
ing determinations  of  vapour-tension  made  at  various  localities  when 
it  is  desired  to  establish  a  rigorous  comparison  between  them. 

278.  Laws  of  Combination  by  Volume. — It  was  discovered  by  Gay- 
Lussac,  that  when  two  or  more  gaseous  elements  at  the  same  tem- 
perature and  pressure  enter  into  chemical  combination  with  each 
other,  the  two  following  laws  apply: — 

1.  The  volumes  of  the  components  bear  a  very  simple  ratio  to  each 
other,  such  as  2  to  3,  1  to  2,  or  1  to  1. 

2.  The  volume  of  the  compound  has  a  simple  ratio  to  the  sum  of 
the  volumes  of  the  components. 

Ammonia,  for  example,  is  formed  by  nitrogen  and  hydrogen  unit- 
ing in  the  proportion  of  one  volume  of  the  former  to  three  of  the 
latter,  and  the  volume  of  the  ammonia,  if  reduced  to  the  same  pres- 
sure as  each  of  its  constituents,  is  just  half  the  sum  of  their  volumes. 
Further  investigation  has  led  to  the  conclusion  (which  is  now  gene- 
rally received,  though  hampered  by  some  apparent  exceptions),  that 
these  laws  apply  to  all  cases  of  chemical  combination,  the  volumes 
compared  being  those  which  would  be  occupied  respectively  by  the 
combining  elements  and  the  compound  which  they  form,  when 
reduced  to  the  state  of  vapour,  at  such  a  temperature  and  pressure 
as  to  be  very  far  removed  from  liquefaction,  and  consequently  to 
possess  the  properties  of  what  we  are  accustomed  to  call  permanent 
gases. 

It  is  obvious  that  if  all  gases  and  vapours  were  equally  expansible 
by  heat,  the  volume-ratios  referred  to  in  this  law  would  be  the  same 
at  all  temperatures ;  and  that,  in  like  manner,  if  they  were  all  equally 
compressible  (whether  obeying  Boyle's  law,  or  departing  equally 
from  it  at  equal  pressures),  the  volume-ratios  would  be  independent 
of  the  pressure  at  which  the  comparison  was  made. 

In  reality  great  differences  exist  between  different  vapours  in  both 
respects,  and  these  inequalities  are  greater  as  the  vapours  are  nearer 
to  saturation.  It  is  accordingly  found  that  the  above  laws  of  volume- 
ratio  often  fail  to  apply  to  vapours  when  under  atmospheric  pressure 
arid  within  a  few  degrees  of  their  boiling-points,  and  that,  in  such 
cases,  a  much  nearer  fulfilment  of  the  law  is  obtained  by  employing 
very  high  temperatures,  or  operating  in  inclosures  at  very  low  pres- 
sures. 

278  A.  Relation  of  Vapour-densities  to  Chemical  Equivalents.— Chem- 


358  MEASUREMENT   OF   THE 

ists  have  determined  with  great  accuracy  the  combining  proportions 
by  weight  of  most  of  the  elements.  Hence  the  preceding  laws  can 
be  readily  tested  for  bodies  which  usually  exist  in  the  solid  or  liquid 
form,  if  we  are  able  to  compare  the  densities  of  their  vapours.  In 
fact,  if  two  such  elements  combine  in  the  ratio,  by  weight,  of  w1  to  w^, 
we  have 


vl  v<i  d^  d2  denoting  the  volumes  and  densities  of  the  vapours  of 
weights  W-L  iv  %  of  the  two  substances. 
Hence  we  have  the  equation  — 


which  gives  the  required  volume-ratio  of  the  vapours,  if  the  ratio  of 
their  densities  be  known. 

The  densities  themselves  will  differ  enormously  according  to  the 
pressure  and  temperature  at  which  they  are  taken,  but  their  ratio 
will  only  vary  by  comparatively  small  amounts,  and  would  not  differ 
at  all  if  they  were  equally  expansible  by  heat,  and  equally  com- 
pressible. Hence  comparison  will  be  facilitated  by  tabulating  the 
ratios  of  the  densities  to  that  of  some  standard  gas,  namely  air,  under 
the  same  conditions  of  pressure  and  temperature,  rather  than  the 
absolute  densities.  This  is  accordingly  the  course  which  is  generally 
pursued,  so  generally  indeed,  that  by  the  vapour-  density  of  a  sub- 
stance is  commonly  understood  the  relative  density  as  measured  by 
this  ratio. 

The  process  most  frequently  employed  for  the  determination  of 
this  element  is  that  invented  by  Dumas. 

*/*  279.  Dumas'  Method.  —  The  apparatus  consists  of  a  glass  globe  B, 
containing  the  substance  which  is  to  be  converted  into  vapour. 

The  globe  is  placed  in  a  vessel  C,  containing  some  liquid  which 
can  be  raised  to  a  suitable  temperature.  If  the  substance  to  be 
operated  on  is  one  which  can  be  vaporized  at  100°  C.,  the  bath  con- 
sists simply  of  boiling  water.  When  higher  temperatures  are 
required,  a  saline  solution,  oil,  or  a  fusible  alloy  is  employed.  In  all 
cases,  the  liquid  should  be  agitated,  that  its  temperature  may  be  the 
same  in  all  parts.  This  temperature  is  indicated  by  the  thermo- 
meter t. 

When  the  substance  in  the  globe  has  attained  its  boiling-point, 
evaporation  proceeds  rapidly,  and  the  vapour  escapes,  carrying  out 


MAXIMUM   TENSIONS   OF   VAPOURS. 


359 


the  air  along  with  it.  When  the  vapour  ceases  to  issue,  we  may 
assume,  if  the  quantity  of  matter  originally  taken  has  been  suffi- 
ciently large,  that  all  the 
air  has  been  expelled,  and 
that  the  globe  is  full  of 
vapour  at  the  temperature 
given  by  the  thermometer, 
and  at  the  external  pres- 
sure H.  The  globe  is  then 
hermetically  sealed  at  the 
extremity  p  of  the  neck, 
which  has  been  previously 
drawn  out  into  a  fine  tube. 
^280.  Calculation  of  the 
Experiment. — As  already 
remarked,  the  densities  of 
vapours  given  in  treatises 
on  chemistry  express  the 
ratio  of  the  weight  of  a  given  volume  of  the  vapour  to  that  of  the 
same  volume  of  air  at  the  same  temperature  and  pressure.  In  order 
to  deduce  this  ratio  from  the  preceding  experiment,  we  must  first  find 
the  weight  of  the  vapour.  This  is  done  by  weighing  the  globe  with 
its  contents,  after  allowing  it  to  cool.  Suppose  the  weight  thus  found 
to  be  W.  Before  the  experiment  the  globe  had  been  weighed  full  of 
dry  air  at  a  known  temperature  t  and  pressure  h.  Suppose  this 
weight  to  be  W;  the  difference  W— -W  evidently  represents  the 
excess  of  the  weight  of  the  vapour  above  that  of  the  air.  If,  then, 
we  add  W  — W  to  the  weight  of  the  air,  we  shall  evidently  have  the 
weight  of  the  vapour.  Now  the  weight  of  the  air  is  easily  deduced 
from  the  known  volume  of  the  globe.  If  V  denote  this  volume  at 
zero  expressed  in  litres,  the  weight  in  grammes  of  the  air  con- 
tained in  the  globe  at  the  time  of  weighing  is 


Fig.  263.— Dumas'  Apparatus. 


1-293  x 


_ 

1  +  at  '  760' 


K  denoting  the  coefficient  of  cubical  expansion  of  glass,  and  a  the 
coefficient  of  expansion  of  air.  The  weight  of  the  vapour  contained 
in  the  globe  is  consequently 

A  =  W-W'  +  V(1  +  KO  x  1-293  x  -1      .  ~. 

Let  H  be  the  pressure,  and  T  the  temperature  at  the  time  cf  sealing 


360  MEASUREMENT   OF  THE 

the  globe.  The  volume  occupied  by  the  vapour  under  these  circum- 
stances was  V(1+KT).  The  density  of  the  vapour  will  therefore 
be  obtained  by  dividing  A  by  the  weight  of  this  volume  of  air  at  the 
same  temperature  and  pressure.  But  this  weight  is 

'     V(1+KT).  1-293..    H.. 


hence,  finally,  the  required  relative  density  is 

l        h 


.1-293. 

'     760 


A' 


The  correctness  of  this  formula  depends  upon  the  assumption  that 
no  air  is  left  in  the  globe.  In  order  to  make  sure  that  this  condi- 
tion is  fulfilled,  the  point  p  of  the  neck  of  the  globe  is  broken  off 
under  mercury;  the  liquid  then  rushes  in,  and,  together  with  the 
condensed  vapour,  fills  the  globe  completely,  if  no  air  has  been  left 
behind. 

This  last  operation  also  affords  a  means  of  calculating  the  volume  V ; 
for  we  have  only  to  weigh  the  mercury  contained  in  the  globe,  or  to 
measure  it  in  a  graduated  tube,  in  order  to  ascertain  its  volume  at 
the  actual  temperature,  whence  the  volume  at  zero  can  easily  be 
deduced. 

.281.  Example. — In  order  better  to  illustrate  the  method,  we  shall 
take  the  following  numerical  results  obtained  in  an  investigation  of 
the  vapour-density  of  sulphide  of  carbon: — 

Excess  of  weight  of  vapour  above  weight  of  air,  W — W  =  *3  gramme; 
temperature  of  the  vapour  T  =  59°;  external  pressure  Hr=7o2'5  milli- 
metres; volume  of  the  globe  at  a  temperature  of  12°,  190  cubic  centi- 
metres; temperature  of  the  dry  air  which  filled  the  globe  at  the  time 

of  weighing,  £=15°;  pressure  7i  =  765;  K=  •TS'-OO* 
The  volume  V  of  the  globe  at  zero  is 

190 

12  -=189-94  cubic  centimetres -'18994  litre. 

"r3570"0 

The  weight  of  the  air  contained  in  the  globe  is 

•18994  x  1-293  .  (l  +  J '- )  .  pj^j^gjjj  -  |f  =  «« 

Weight  of  the  vapour, 

•23658  +  W  -  W'=  -53658  gramme. 


MAXIMUM  TENSIONS   OF  VAPOURS. 


361 


The  weight  of  the  same  volume  of  air  at  the  same  temperature  and 
pressure  is 


•18994x1-293 


59 


, _ 1^.±  =  -20019  gramme. 

38700/     1  +  -00366x59      760 

The  density  is  therefore 


'53658 
20019 


Deville  and  Troost  have  effected  several  improvements  in  the  appli- 
cation of  Dumas'  method  to  vapours  at  high  temperatures.  These 
temperatures  are  obtained  by  boiling  various  substances,  such  as 
chloride  of  zinc,  cadmium,  which  boils  at  860°  C.,  or  zinc,  which  boils 
at  104  0°C.  For  temperatures  above  800°,  the  glass  globe  is  replaced 
by  a  globe  of  porcelain,  which  is  hermetically  sealed  with  the  oxyhy- 
drogen  blowpipe.  The  globe  itself  serves  as  a  pyrometer  to  deter- 
mine the  temperature;  and  since  the  weight  of  air  becomes  very 
inconsiderable  at  high  temperatures,  some  heavier  vapour,  such  as 
that  of  iodine,  is  substituted  in  its  place.  If  we  suppose,  as  we  may 
fairly  do,  that  at  these  high  temperatures  the  coefficient  of  expansion 
of  the  vapour  of  iodine  is  the  same  as  that  of  air,  the  temperature 
may  easily  be  deduced  from  the  weight  of  iodine  contained  in  the 
globe.  We  subjoin  a  table  of  some  relative  densities  of  vapours 
obtained  by  this  method: — 


Water, 0'622 

Alcohol, 1-6138 

Ether, 2  "586 

Spirit  of  turpentine,     .     .  /i'0130 

Iodine, 8716 

Sulphur, 2-23 


Phosphorus, 4 '5 

Cadmium, 3'94 

Chloride  of  aluminium,  .     .     9'34< 
Bromide  of  aluminium,       .  18 '62 
Chloride  of  zirconium,   .     .     8'1 
Sesquichloride  of  iron,    .     .  11 '39 


282.  Limiting  Values  of  Relative  Densities. — In  investigating  the 
relative  density  of  acetic  acid  vapour,  Cahours  found  that  it  went 
on  decreasing  as  the  temperature  increased,  up  to  a  certain  point, 
after  which  no  further  change  was  observable.  A  similar  circum- 
stance is  observed  in  the  case  of  all  substances,  only  in  different 
degrees.  The  vapour  of  sulphur,  for  instance,  has  a  relative  density 
of  6'65  at  500°  Q,  while  at  about  1000°  C.  it  is  only  223.  This 
indicates  that  the  vapours  in  question  are  more  expansible  by  heat 
than  air  until  the  limiting  temperatures  are  attained.  Indeed  it  may 
be  laid  down  as  a  general  principle,  that  the  nearer  a  vapour  is  to 
saturation  the  greater  is  the  change  produced  in  its  absolute  density 
by  a  given  change  whether  of  temperature  or  pressure.  The  limiting 
density-ratio  is  always  that  which  it  is  most  important  to  determine, 


362 


MEASUREMENT   OF  THE 


and  we  should  consequently  take  care  that  the  temperature  of  the 
vapour  is  sufficiently  high  to  enable  us  to  obtain  it. 

283.  Gay-Lussac's  Method. — Gay-Lussac  determined  the  density  of 
the  vapour  of  water  and  of  some  other  liquids  by  a  method  a  little 
more  complicated  than  that  described  above,  and  which  for  that 
reason  has  not  been  generally  adopted  in  the  laboratory.  We  proceed 
to  describe  it,  however,  on  account  both  of  its  historical  interest  and 
of  the  importance  of  the  question  which  it  has  assisted  in  solving. 

A  graduated  tube  divided  into  cubic  centimetres,  suppose,  is  filled 
with  mercury,  and  inverted  in  a  cast-iron  vessel  containing  the  same 
liquid.  The  inverted  tube  is  surrounded  by  a  glass  envelope  con- 
taining water,  as  in  Dalton's  apparatus.  A  small  glass  bulb  contain- 
ing a  given  weight  w  (expressed  in  grammes)  of  distilled  water  is 
passed  into  the  tube,  and  rises  to  the  surface  of  the  mercury.  The 

temperature  of  the  apparatus  is  then 
raised  by  means  of  a  fire  below,  the  bulb 
bursts,  and  the  water  which  it  contained 
is  converted  into  vapour.  If  the  quan- 
tity of  water  be  not  too  great,  it  is  all 
eon  verted  into  vapour;  this  is  known 
to  be  the  case  when,  at  the  temperature 
of  about  100°,  the  mercury  stands  higher 
in  the  tube  than  in  the  vessel,  for  if 
there  were  any  liquid-water  present, 
the  space  would  be  saturated,  and  the 
tension  of  the  vapour  would  be  equal  to 
the  external  pressure.  This  arrange- 
ment accordingly  gives  the  weight  of  a 
known  volume  of  the  vapour  of  water. 

This  volume,  which  may  at  once  be  read  upon  the  graduated  tube,  is 
equal  to  V  (1  +  KT),  Y  being  the  number  of  divisions  occupied  by 
the  vapour.  The  temperature  T  is  marked  by  a  thermometer  im- 
mersed in  the  water  contained  in  the  envelope.  The  tension  of  the 
vapour  is  evidently  equal  to  the  external  pressure  minus  the  height 
of  the  mercury  in  the  tube. 

In  order  to  find  the  relative  density,  we  must  divide  w  by  the 
weight  of  a  volume  V  (1 +KT)  of  air  at  the  temperature  T  and  pres- 
sure H  —  h,  giving 


Fig.  264. — Gay-Lussac's  Apparatus. 


V  (1  +  KT)  x -001293  x 


1         H-& 
1  +  aT'    760"' 


MAXIMUM  TENSIONS  OF  VAPOURS.  363 

The  relative  density  of  the  vapour  of  water,  as  thus  determined  by 
Gay-Lussac,  is  about  -§-,  or  '625.  Several  recent  investigations  have 
given  as  mean  result  '622,  which  agrees  with  the  theoretical  density 
deduced  from  the  composition  of  water.1 

284.  Volume  of  Vapour  formed  by  a  given  Weight  of  Water.— When 
the  density  of  the  vapour  of  water  is  known,  the  increase  of  volume 
which  occurs  when  a  given  quantity  of  water  passes  into  the  state 
of  vapour  may  easily  be  calculated.  Suppose,  for  instance,  that  we 
wish  to  find  the  volume  which  a  cubic  centimetre  of  water  at  4°  will 
occupy  in  the  state  of  vapour  at  100°.  At  this  temperature  the 
tension  of  the  vapour  is  equal  to  one  atmosphere,  and  its  weight  is 
equal  to  '622  times  the  weight  of  the  same  volume  of  air  at  the  same 
temperature  and  pressure.  If  then  V  be  the  volume  in  litres,  we 
have  (in  grammes) 


whence 


V  x  1-293  x —  x  -622=1, 

l+100a 


V=  A±l°0a_  =J'366  =1-698  lit.  =  1698  cubic  centimetres. 
1-293  x -622     -804246 


Hence  we  see  that  water  at  4°  gives  about  1700  times  its  volume  of 
vapour  at  100°C. 

The  latent  heat  of  evaporation  is  doubtless  connected  with  this 
increase  of  volume ;  and  it  may  be  remarked  that  both  these  elements 
appear  to  be  greater  for  water  than  for  any  other  substance. 

1  Water  is  composed  of  2  volumes  of  hydrogen,  and  1  volume  of  oxygen,  forming  2 
volumes  of  vapour  of  water.  The  sum  of  the  density  of  oxygen  and  twice  the  density  of 
hydrogen  is  1*244,  and  the  half  of  this  is  exactly  '622.— D. 


CHAPTER    XXVIII 


IIYGROMETllY. 


^  285.  Humidity. — The  condition  of  the  air  as  regards  moisture 
involves  two  distinct  elements:  (1)  the  amount  of  vapour  present 
in  the  air,  and  (2)  the  ratio  of  this  to  the  amount  which  would 
saturate  the  air  at  the  actual  temperature.  It  is  upon  the  second  of 
these  elements  that  our  sensations  of  dryness  and  moisture  chiefly 
depend,  and  it  is  this  element  which  meteorologists  have  agreed  to 
denote  by  the  term  humidity;  or,  as  it  is  sometimes  called,  relative 
humidity.  It  is  usually  expressed  as  a  percentage ;  for  example,  if 
the  weight  of  vapour  present  is  seven-tenths  of  that  required  for 
saturation,  the  humidity  is  said  to  be  70. 

The  words  humid  and  'moist,  as  applied  to  air  in  ordinary  lan- 
guage, nearly  correspond  to  this  technical  use  of  the  word  humidity; 
and  air  is  usually  said  to  be  dry  when  its  humidity  is  considerably 
below  the  average.  In  treatises  on  physics,  "dry  air"  usually 
denotes  air  whose  humidity  is  zero. 

The  air  in  a  room  heated  by  a  hot  stove  contains  as  much  vapour 
weight  for  weight  as  the  open  air  outside;  but  it  is  drier,  because  its 
capacity  for  vapour  is  greater.  In  like  manner  the  air  is  drier  at 
noon  than  at  midnight,  though  the  amount  of  vapour  present  is  about 
the  same;  and  it  is  for  the  most  part  drier  in  summer  than  in  winter, 
though  the  amount  of  vapour  present  is  much  greater. 

Bearing  in  mind  that  a  cubic  foot  of  air  is  able  to  take  up  the  same 
amount  of  vapour  as  a  cubic  foot  of  empty  space,  we  may  define  the 
humidity  of  the  air  as  the  weight  of  aqueous  vapour  in  a  given 
volume  of  air,  expressed  as  a  percentage  of  the  weight  of  vapour 
at  saturation  which  would  occupy  the  same  volume  at  the  actual 
temperature, 

Also,  since  aqueous  vapour  nearly  fulfils  Boyle's  law,  the  humidity 


THE   DEW-POINT.  365 

of  the  air  may  be  obtained  by  comparing  the  tension  of  the  vapour 
present  in  the  air  with  the  maximum  tension  for  the  actual  tempera- 
ture. 

^s  288.  Dew-point.  —  When  air  containing  aqueous  vapour  is  gradually 
cooled  at  constant  pressure,  its  density  increases,  and  the  rate  of 
increase  is  sensibly  the  same  for  the  vapour  as  for  the  dry  air  with 
which  it  is  mixed  (inasmuch  as  vapours  not  in  contact  with  their 
liquids  nearly  fulfil  Gay-Lussac's  law),  until  a  point  is  reached  at 
which  the  density  of  the  vapour  becomes  equal  to  the  maximum 
density  corresponding  to  the  temperature.  This  temperature  is  called 
the  dew-point  of  the  given  mass,  and  any  further  reduction  of  tem- 
perature will  be  accompanied  by  the  condensation  of  a  portion  of  the 
vapour,  which  will  take  the  form  of  dew,  rain,  snow,  or  hoar-frost, 
according  to  circumstances.  If  the  cooling  is  produced  by  the  low 
temperature  of  the  sides  of  the  containing  vessel,  the  deposit  will  be 
dew  or  hoar-frost,  according  as  the  temperature  of  the  sides  is  above 
or  below  the  freezing-point.  If  the  cooling  takes  place  in  the 
interior  of  the  mass  of  air,  the  deposit  will  be  rain  or  snow,  accord- 
ing as  the  temperature  of  deposition  is  above  or  below  the  freezing- 
point. 

In  the  operation  of  cooling  down  to  the  dew-point,  the  density  of 
the  vapour,  as  we  have  seen,  increases.  Let  t  denote  the  initial 
temperature,  and  T  the  dew-point,  and  let  d  and  D  be  the  densities 
of  the  vapour  at  these  temperatures.  Then  we  have,  by  Gay-Lussac's 
law, 


. 

1  +  aT 

But  the  tension  of  the  vapour  is  not  sensibly  changed  by  the  opera- 
tion, since  the  whole  pressure  is  by  hypothesis  preserved  constant, 
and  the  changes  of  temperature  and  volume  affect  the  dry  and  the 
vaporous  constituent  nearly  alike. 

If  the  reduction  of  temperature  from  t  to  T  took  place  at  constant 
volume  (in  a  closed  receiver,  for  example),  we  should  then  have 


p  and  P  denoting  the  vapour-tensions  at  the  temperatures  t  and  T; 
and  the  density  would  remain  constant,  since  no  vapour  enters  or 
escapes.  In  this  case  the  vapour  would  not  begin  to  be  condensed 
till  a  somewhat  lower  temperature  had  been  attained. 

Hygroscopes.  —  Anything  which  serves  to  give  rough  indica- 


366 


HYGROMETRY. 


tions  of  the  state  of  the  air  as  regards  moisture  may  be  called  a 
hygroscope  (vypog,  moist).  Many  substances,  especially  those  which 
are  composed  of  organic  tissue,  have  the  property  of  absorbing  the 
moisture  of  the  surrounding  air,  until  they  attain  a  condition  of 
equilibrium,  such  that  their  affinity  for  the  moisture  absorbed  is 
exactly  equal  to  the  force  with  which  the  latter  tends  to  evaporate. 
Hence  it  follows  that,  according  to  the  dampness  or  dryness  of  the 
air,  such  a  substance  will  absorb  or  give  up  vapour,  either  of  which 
processes  is  always  attended  with  a  variation  in  the  dimensions  of  the 
body.  The  nature  of  this  variation  depends  upon  the  peculiar  struc- 
ture of  the  substance;  thus,  for  instance,  bodies  formed  of  filaments 
exhibit  a  greater  increase  in  the  direction  of  their  breadth  than  of 
their  length.  Membranous  bodies,  on  the  other  hand,  such  as  paper 
or  parchment,  formed  by  an  interlacing  of  fibres  in  all  directions, 
expand  or  contract  almost  as  if  they  were  homogeneous.  Bodies 
composed  of  twisted  fibres,  as  ropes  and  strings,  swell  under  the 
action  of  moisture,  grow  shorter,  and  are  more  tightly  twisted.  The 
opposite  is  the  case  with  catgut,  which  is  often  employed  in  popular 
hygroscopes. 

288.  Hygrometers. — Instruments  intended  for  furnishing  precise 
measurements  of  the  state  of  the  air  as  regards  moisture  are  called 
hygrometers.  They  may  be  divided  into  four  classes: — 

1.  Hygrometers  of  absorption,  which  should  rather  be  called 
hygroscopes. 

2.  Hygrometers  of  condensation,  or  dew-point 
instruments. 

3.  Hygrometers  of  evaporation,   or  wet  and 
dry  bulb  thermometers. 

4.  Chemical  hygrometers,  for  directly  measur- 
ing the  weight  of  vapour  in  a  given  volume  of 
air. 

289.    De    Saussure's   Hygrometer. — The   best 
hygrometer  of  absorption  is  that  of  De  Saussure, 
consisting  of  a  hair  deprived  of  grease,  which  by 
its  contractions  moves  a  needle  (Fig.  266).    When 
the  hair  relaxes,  the  needle  is  caused  to  move  in 
De  saussurfs^Hygroscope.     the  opposite  direction  by  a  weight,  which  serves 
to  keep  the  hair  always  equally  tight.     The  hair 
contracts  as  the  humidity  increases,  but  not  in  simple  proportion, 
and  Regnault's  investigations   have  shown  that,   unless  the  most 


DEW-POINT   HYGROMETERS. 


367 


Fig.  267.— Monnier's  Hygroscope. 


minute  precautions  are  adopted  in  the  construction  and  graduation 
of  each  individual  instrument,  this  hygrometer  will  not  furnish 
definite  numerical  measures. 

Fig.  267  represents  Mon- 
nier's modification  of  De  Saus- 
sure's  hygrometer,  in  which 
the  hair,  after  passing  over 
four  pulleys,  is  attached  to  a 
light  spring,  which  serves  in- 
stead of  a  weight,  and  gives 
the  advantage  of  portabi- 
lity. 

These  instruments  are  never 
employed  for  scientific  pur- 
poses in  this  country. 
)  290.  Dew-point  Hygrometers. 
— These  are  instruments  for 
the  direct  observation  of  the 
dew-point,  by  causing  moist- 
ure to  be  condensed  from  the 

air  upon  the  surface  of  a  body  artificial^  cooled  to  a  known  tempera- 
ture. 

The  dew-point,  which  is  itself  an  important  element,  gives  di- 
rectly, as  we  have  seen  in  §  286,  the  tension  of  vapour;  and  if  the 
temperature  of  the  air  is  at  the  same  time  observed,  the  tension 
requisite  for  saturation  is  known.  The  ratio  of  the  former  to  the 
latter  determines  the  humidity. 

The  principle  of  these  instruments  may  be  illustrated  by  a  descrip- 
tion of  their  simplest  type,   the  hygrometer  of  Leroy,   a  French 
philosopher  of  the  last  century. 
d    291.  Leroy's  Hygrometer. — The  instrument  con- 
sists of  a  tin  vessel  containing  water,  in  which  a 
thermometer  is  immersed.     The  temperature  of 
the  water  and   containing  vessel   is   gradually 
lowered  by  the  introduction  of  ice,  and  when  it 
has  fallen  below  the  dew-point  of  the  adjacent 
air,  a  portion  of  the  vapour  will  be  condensed  as 
dew  upon  the  exterior  of  the  vessel.     This  is  at  once  recognized  by 
the  metallic  surface  losing  its  brilliancy. 

We  may  observe  that  the  deposition  of  dew  does  not  begin  till  the 


Fig.  268. 
Leroy's  Hygrometer. 


368  HYGROMETRY. 

point  of  saturation  has  been  passed,  and  that  the  indication  of  the 
thermometer  is  consequently  somewhat  too  low.  Leroy  proposed  an 
empirical  correction  of  half  a  degree.  There  are,  however,  other 
defects  in  the  instrument ;  the  use  of  ice  does  not  afford  a  speedy 
and  regular  diminution  of  temperature;  and  it  is  especially  objection- 
able to  place  an  open  vessel  containing  water  in  the  very  place  where 
the  humidity  of  the  air  is  to  be  determined. 

S-  292.  Daniell's  Hygrometer. — Daniell's  hygrometer  is  an  instrument 
of  much  greater  precision,  and  has  been  very  extensively  used.     It 
consists  of  a  bent  tube  with  a  globe  at  each  end,  and  is  partly  filled 
with  ether.     The  rest  of  the  space  is  occupied  with  vapour  of  ether, 
the   air   having   been   expelled.      One  of  the 
globes  A  contains  a  thermometer  t.    This  globe 
I  I     ^  tiiu       *s  genera^y  made  of  black  glass,  which  presents 
^*^        a  brilliant  surface.     The  method  of  using  the 
instrument  is  as  follows: — The  whole  of  the 


liquid  is  first  passed  into  the  globe  A,  and  then 
wP   41p  ^ne  °^ner  gl°be  B,  which  is  covered  with  muslin, 

is  moistened  externally  with  ether.  The  ev.apo- 
ration  of  this  ether  from  the  muslin  causes  a 
partial  condensation  of  vapour  of  ether  in  the 
Danieii'sgkygrometer.  interior  of  the  globe,  which  produces  a  fresh 
evaporation  from  the  surface  of  the  liquid  in  A, 

thus  lowering  the  temperature  of  that  part  of  the  instrument.  By 
carefully  watching  the  surface  of  the  globe,  the  exact  moment  of 
the  deposition  of  dew  may  be  ascertained.  The  temperature  is  then 
read  on  the  inclosed  thermometer.  This  temperature  is  a  little  lower 
than  the  dew-point. 

^  >S         If  the  instrument  be  now  left  to  itself,  the  exact  moment  of  the 
i  W-  disappearance  of  the  dew  may  be  observed;  this  corresponds  to  an 
I  ^     indicated  temperature  a  little  above  the  dew-point,  and  the  usual 
plan  is  to  take  the  mean  between  this  temperature  and  that  first 
observed.     The  temperature  of  the  surrounding  air  is  given  by  a 
thermometer  if  attached  to  the  stand. 

Daniell's  hygrometer,  though  capable  of  furnishing  accurate  in- 
dications, has  some  defects,  which  have  been  removed  by  the  improve- 
ments effected  by  Regnault. 

293.  Regnault's  Hygrometer. — Regnault's  hygrometer  consists  (Fig. 
270)  of  a  glass  tube  closed  at  the  bottom  by  a  very  thin  silver  cap  D. 
The  opening  at  the  upper  end  is  closed  by  a  cork,  through  which 


REGNAULT'S  HYGROMETER. 


369 


passes  the  stem  of  a  thermometer  T,  and  a  glass  tube  t  open  at  both 
ends.  The  lower  end  of  the  tube  and  the  bulb  of  the  thermometer 
dip  into  ether  contained  in  the  silver  cap.  A  side  tube  establishes 
communication  between  this  part  of  the  apparatus  and  a  vertical 
tube  UV,  which  is  itself  connected  with  an  aspirator1  A,  placed  at  a 


Fig.  270. — Regnault's  Hygrometer. 

convenient  distance.  By  allowing  the  water  in  the  aspirator  to 
escape,  a  current  of  air  is  produced  through  the  ether,  which  has  the 
effect  of  keeping  the  liquid  in  agitation,  and  thus  producing  uniform-  -jC 
ity  of  temperature  throughout  the  whole.  It  also  tends  to  hasten 
evaporation;  and  the  cold  thus  produced  speedily  causes  a  deposition 
of  dew,  which  is  observed  from  a  distance  with  a  telescope,  thus 
obviating  the  risk  of  vitiating  the  observation  by  the  too  close 
proximity  of  the  observer.  The  observation  is  facilitated  by  the 
contrast  offered  by  the  appearance  of  the  second  cap,  which  has  no  ^-v^^ 
communication  with  the  first,  and  contains  a  thermometer  for  giving 
the  temperature  of  the  external  air.  By  regulating  the  flow  of  liquid 
from  the  aspirator,  the  temperature  of  the  ether  can  be  very  nicely 
controlled,  and  the  dew  can  be  made  to  appear  and  disappear  at 
temperatures  nearly  identical.  The  mean  of  the  two  will  then  very 
accurately  represent  the  dew-point. 

The  liquid  employed  in  Regnault's  hygrometer  need  not  be  ether. 

1  An  aspirator  is  a  vessel  into  which  air  is  sucked  at  the  top  to  supply  the  place  of  water 
which  is  allowed  to  escape  at  the  bottom;  or,  more  generally,  it  is  any  apparatus  for  sucking 
in  air  or  gas. 

24 


370 


HYGROMETRY. 


Alcohol,  a  much  less  volatile  liquid,  will  suffice.  This  is  an  important 
advantage ;  for,  since  the  boiling-point  of  ether  is  36°  C.  (97°  F.),  it  is 
not  easy  to  preserve  it  in  hot  climates. 

k  294.  Wet  and  Dry  Bulb  Hygrometer. — This  instrument,  which  is 
also  called  Mason's  hygrometer,  and  is  known  on  the  Continent  as 
August's  psychrometer,  consists  (Fig.  271)  of  two  precisely  similar 
thermometers,  mounted  at  a  short  distance  from  each  other,  the  bulb 

of  one  of  them  being  covered  with  muslin, 
which  is  kept  rnoist  by  means  of  a  cotton 
wick  leading  from  a  vessel  of  water.  The 
evaporation  which  takes  place  from  the 
moistened  bulb  produces  a  depression  of 
temperature,  so  that  this  thermometer  reads 
lower  than  the  other  by  an  amount  which 
increases  with  Jhe  dryness  of  the  air.  The 
instrument  must  be  mounted  in  such  a  way 
that  the  air  can  circulate  very  freely  around 
the  wet  bulb;  and  the  vessel  containing  the 
water  should  be  small,  and  should  be  placed 
some  inches  to  the  side.  The  level  of  this 
vessel  must  be  high  enough  to  furnish  a 
supply  of  water  which  keeps  the  muslin 
thoroughly  moist,  but  not  high  enough  to 
cause  a  drop  to  form  at  the  bottom  of  the 
bulb.  Unless  these  precautions  are  observed, 
the  depression  of  temperature  will  not  be 
sufficiently  great,  especially  in  calm  weather. 
In  frosty  weather  the  wick  ceases  to  act, 
and  the  bulb  must  be  dipped  in  water  some  time  before  taking  an 
observation,  so  that  all  the  water  on  the  bulb  may  be  frozen,  and  a 
little  time  allowed  for  evaporation  from  the  ice  before  the  reading  is 
taken. 

The  great  facility  of  observation  afforded  by  this  instrument  has 
brought  it  into  general  use,  to  the  practical  exclusion  of  other  forms 
of  hygrometer.  As  the  theoretical  relation  between  the  indications 
of  its  two  thermometers  and  the  humidity  as  well  as  the  dew-point 
of  the  air  is  rather  complex,  and  can  scarcely  be  said  to  be  known 
with  certainty,  it  is  usual,  at  least  in  this  country,  to  effect  the 
reduction  by  means  of  tables  which  have  been  empirically  constructed 
by  comparison  with  the  indications  of  a  dew-point  instrument.  The 


Fig.  271. 
Wet  and  Dry  Thermometers. 


WET  AND  DRY   BULB   HYGROMETER.  371 

tables  universally  employed  by  British  observers  were  constructed 
by  Mr.  Glaisher,  and  are  based  upon  a  comparison  of  the  simultaneous 
readings  of  the  wet  and  dry  bulb  thermometers  and  of  Daniell's 
hygrometer  taken  for  a  long  series  of  years  at  Greenwich  observatory, 
combined  with  some  similar  observations  taken  in  India  and  at 
Toronto.1 

According  to  these  tables,  the  difference  between  the  dew-point 
and  the  wet-bulb  reading  bears  a  constant  ratio  to  the  difference 
between  the  two  thermometers,  when  the  temperature  of  the  dry- 
bulb  thermometer  is  given.  When  this  temperature  is  53°  F.,  the 
dew-point  is  as  much  below  the  wet-bulb  as  the  wet-bulb  is  below 
the  temperature  of  the  air.  At  higher  temperatures  the  wet-bulb 
reading  is  nearer  to  the  dew-point  than  to  the  air-temperature,  and 
the  reverse  is  the  case  at  temperatures  below  53°. 

In  order  to  obtain  a  clue  to  the  construction  of  a  rational  formula 
for  deducing  the  dew-point  from  the  indications  of  this  instrument,  -  *~<~ 
we  shall  assume  that  the  wet-bulb  is  so  placed  that  its  temperature  I  / 
is  not  sensibly  affected  by  radiation  from  surrounding  objects,  and 
hence  that  the  heat  which  becomes  latent  by  the  evaporation  from 
its  surface  is  all  supplied  by  the  surrounding  air.  When  the  tem- 
perature of  the  wet-bulb  is  falling,  heat  is  being  consumed  by  eva- 
poration faster  than  it  is  supplied  by  the  air;  and  the  reverse  is  the 
case  when  it  is  rising.  It  will  suffice  to  consider  the  case  when  it  is 
stationary,  and  when,  consequently,  the  heat  consumed  by  evapo- 
ration in  a  given  time  is  exactly  equal  to  that  supplied  by  the 
air. 

Let  t  denote  the  temperature  of  the  air,  which  is  indicated  by  the 
dry-bulb  thermometer;  if  the  temperature  of  the  wet-bulb;  T  the 
temperature  of  the  dew-point,  and  let/,/,  F  be  the  vapour- tensions 
corresponding  to  saturation  at  these  three  temperatures.  Then,  as 
shown  in  §  286,  the  tension  of  the  vapour  present  in  the  air  at  its 
actual  temperature  t  is  also  equal  to  F. 

We  shall  suppose  that  wind  is  blowing,  so  that  continually  fresh 
portions  of  air  come  within  the  sphere  of  action  of  the  wet-bulb. 
Then  each  particle  of  this  air  experiences  a  depression  of  temperature 
and  an  increase  of  vapour-tension  as  it  comes  near  the  wet-bulb,  from 
both  of  which  it  afterwards  recovers  as  it  moves  away  and  mixes 
with  the  general  atmosphere. 

1  The  first  edition  of  these  Tables  differs  considerably  from  the  rest,  and  is  never  used; 
but  there  has  been  no  material  alteration  since  the  second  edition  (1556). 


372  HYGROMETRY. 

If  now  it  is  legitimate  to  assume1  that  this  depression  of  tempera- 
ture and  exaltation  of  vapour-tension  are  always  proportional  to  one 
another,  not  only  in  comparing  one  particle  with  itself  at  different 
times,  but  also  in  comparing  one  particle  with  another,  we  have  the 
means  of  solving  our  problem ;  at  all  events,  if  we  may  make  the 
additional  assumptions  that  a  portion  of  the  air  close  to  the  wet- 
bulb  is  at  the  temperature  of  the  wet-bulb,  and  is  saturated. 

On  these  assumptions  the  greatest  reduction  of  temperature  of  the 
air  is  t  —  t',  and  the  greatest  increase  of  vapour-tension  is/'  — F,  and 
the  corresponding  changes  in  the  whole  mass  are  proportional  to 
these.  The  three  temperatures  t,  t',  T  must  therefore  be  so  related, 
that  the  heat  lost  by  a  mass  of  air  in  cooling  through  the  range  t  —  t', 
is  just  equal  to  the  heat  which  becomes  latent  in  the  formation  of  as 
much  vapour  as  would  raise  the  vapour-tension  of  the  mass  by  the 
amount  /'— F. 

Let  h  denote  the  height  of  the  barometer,  s  the  specific  heat  of 
air  (Chap,  xxxi.),  D  the  relative  density  of  vapour  (§  278 A.),  L  the 
latent  heat  of  steam. 

Then  the  mass  of  the  air  is  to  that  of  the  vapour  required  to  pro- 
duce the  additional  tension,  as  h  to  D  (/'— F),  and  we  are  to  have 

LD  (/-F)  =«(*-«')  h, 
or 

f'-F  =  (t-t')h.JL,  (1) 

which  is  the  required  formula,  enabling  us,  with  the  aid  of  a  table 
of  vapour- tensions,  to  determine  F,  and  therefore  the  dew-point  T, 
when  the  temperatures  t,  t'  of  the  dry  and  wet  bulb,  and  the  height  h 
of  the  barometer,  have  been  observed.  The  expression  for  the  rela- 

~F 

tive  humidity  will  be  j  100. 

Properly  speaking,  s  denotes  the  specific  heat  not  of  dry  air  but  of 
air  containing  the  actual  amount  of  vapour,  and  therefore  depends 
to  some  extent  upon  the  very  element  which  is  to  be  determined ; 
but  its  variation  is  inconsiderable.  L  also  varies  with  the  known 

1  The  assumption  which  Dr.  Apjohn  actually  makes  is  as  follows: — "When  in  the  moist- 
bulb  hygrometer  the  stationary  temperature  is  attained,  the  caloric  which  vaporizes  the 
water  is  necessarily  exactly  equal  to  that  which  the  air  imparts  in  descending  from  the 
temperature  of  the  atmosphere  to  that  of  the  moistened  bulb ;  and  the  air  which  has  under- 
gone this  reduction  becomes  saturated  with  moisture''  (Trans.  R.I. A.  Nov.  1834). 

This  implies  that  unless  air  passes  near  enough  to  the  wet-bulb  to  become  completely 
saturated,  it  experiences  no  depression  of  temperature  whatever — a  very  harsh  supposition; 
but  August  independently  makes  the  same  assumption. 


CHEMICAL   HYGROMETER. 


373 


quantity  t't  but  its  variations  are  also  small  within  the  limits  which 
occur  in  practice.  The  factor  j^  may  therefore  be  regarded  as  con- 
stant, and  its  value,  as  adopted  by  Dr.  Apjohn  for  the  Fahrenheit 
scale,  is  261-  or  ^  x  ^-  We  thus  obtain  what  is  known  as  Apjohn  s 

formula, 

f  _  f     f, 

(2) 


87 


- 

30' 


When  the  wet-bulb  is  frozen,  L  denotes  the  sum  of  the  latent  heats 
of  liquefaction  and  vaporization,  and  the  formula  becomes 


. 

96       30 


(3) 


In  calm  weather,  and  also  in  very  dry  weather,  the  humidity,  as 
deduced  from  observations  of  wet  and  dry  thermometers,  is  generally 
too  great,  probably  owing  mainly  to  the  radiation  from  surrounding 
objects  on  the  wet-bulb,  which  makes  its  temperature  too  high. 
/^295.  Chemical  Hygrometer. — The  determination  of  the  quantity  of 
aqueous  vapour  in  the  atmosphere  may  be  effected  by  ordinary 
chemical  analysis  in  the  following  manner: — 

An  aspirator  A,  of  the  capacity  of  about  50  litres,  communicates  at 
its  upper  end  with  a  system  of  U- tubes  1,  2,  3,  4,  5,  6,  filled  with 


Fig.  272.— Chemical  Hygrometer. 


pieces  of  pumice  soaked  in  sulphuric  acid.     The  aspirator  being  full 
of  water,  the  stop-cock  at  the  bottom  is  opened,  and  the  air  which 


374  HYGROMETRY. 

enters  the  aspirator  to  take  the  place  of  the  water  is  obliged  to  pass 
through  the  tubes,  where  it  leaves  all  its  moisture  behind.  This 
moisture  is  deposited  in  the  first  tubes  only.  The  last  tube  is 
intended  to  absorb  any  moisture  that  may  come  from  the  aspirator. 
Suppose  w  to  be  the  increase  of  weight  of  the  first  tubes  4,  5,  6 ;  this 
is  evidently  the  weight  of  the  aqueous  vapour  contained  in  the  air 
which  has  passed  through  the  apparatus.  The  volume  V  of  this  air, 
which  we  will  suppose  to  be  expressed  in  litres,  may  easily  be  found 
by  measuring  the  amount  of  water  which  has  escaped.  This  air 
has  been  again  saturated  by  contact  with  the  water  of  the  aspirator, 
and  the  aqueous  vapour  contained  in  it  is  consequently  at  the  maxi- 
mum tension  corresponding  to  the  temperature  indicated  by  a  ther- 
mometer attached  to  the  apparatus.  Let  this  tension  be  denoted 
by/.  The  volume  occupied  by  this  air  when  in  the  atmosphere, 
where  the  temperature  is  T,  is  known  by  the  regular  formulae  to  have 
been 

v     H-/     1+aT 
'  H  -  x  '  I  +  at  ' 

x  denoting  the  tension  of  the  aqueous  vapour  in  the  atmosphere,  and 
H  the  total  atmospheric  pressure  as  indicated  by  the  barometer ;  and, 
since  the  relative  density  of  steam  is  *622,  and  the  weight  of  a  litre 
of  air  at  temperature  0°  C.  and  pressure  760  mm.  is  T293  gramme, 
the  weight  of  vapour  which  this  air  contained  must  have  been 

V>H-/   i_+oTxl.293x.622   ^       r 

H-*     l  +  at  760     1+aT 

which  must  be  equal  to  the  known  weight  w,  and  thus  we  have  an 
equation  from  which  we  find 

x  =  w  ( ]  +«0  760  H 

V  (H-/)  x  -622xl-293  +  w  (l+at)  760* 

A  good  approximation  will  be  obtained  by  writing 


whence 


=  945". 


This  method  has  all  the  exactness  of  a  regular  chemical  analysis, 
but  it  involves  great  labour,  and  is,  besides,  incapable  of  showing 
the  sudden  variations  which  often  occur  in  the  humidity  of  the 
atmosphere.  It  can  only  give  the  mean  quantity  of  moisture  in  a 
given  volume  of  air  during  the  time  occupied  by  the  experiment. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 
WEIGHT   OF   MOIST   AIR.  375 

Its  accuracy,  however,  renders  it  peculiarly  suitable  for  checking  the 
results  obtained  by  other  methods. 

296.  Weight  of  a  given  Volume  of  Moist  Air. — The  laws  of  vapours 
and  the  known  formulae  of  expansion  enable  us  to  solve  a  problem 
of  very  frequent  occurrence,  namely,  the  determination  of  the  weight 
of  a  given  volume  of  moist  air.  Let  V  denote  the  volume  of  this 
air,  H  its  pressure,  /  the  tension  of  the  vapour  of  water  in  it,  and  t 
its  temperature.  The  entire  gaseous  mass  may  be  divided  into  two 
parts,  a  volume  V  of  dry  air  at  the  temperature  t  and  the  pressure 
H— /,  whose  weight  is,  by  the  known  formulae, 

V  x  1  -293  x  — —  .  ?— ^j 
L  +  at       760 

and  a  volume  V  of  aqueous  vapour  at  the  temperature  t  and  the 
pressure  /;  the  weight  of  this  latter  is 

-Vx  1-293 x-—  .  -£-. 

8  l  +  at     760 

The  sum  of  these  two  weights  is  the  weight  required,  viz. 

i       H-l/ 

Vxl. 293  ,___.__._. 

Ratio  of  the  Volumes  occupied  by  the  same  Air  when  saturated 
at  Different  Temperatures  and  Pressures. — Suppose  a  mass  of  air  to 
be  in  presence  of  a  quantity  of  water  which  keeps  it  always  saturated; 
let  H  be  the  total  pressure  of  the  saturated  air,  t  its  temperature,  and 
V  its  volume. 

At  a  different  temperature  and  pressure  t'  and  H',  the  volume 
occupied  V  will  in  general  be  different.  The  two  quantities  V  and 
V  may  be  considered  as  the  volumes  occupied  by  a  mass  of  dry  air 
at  temperatures  t  and  if  and  pressures  H— /  and  H'— •/';  we  have  then 
(8  201)  the  relation 

V_H'-/'     l  +  at  (1) 


In  passing  from  one  condition  of  temperature  and  pressure  to  another, 
it  may  be  "necessary,  for  the  maintenance  of  saturation,  that  a  new 
quantity  of  vapour  should  be  formed,  or  that  a  portion  of  the  vapour 
should  be  condensed,  or  again,  neither  the  one  nor  the  other  change 
may  take  place.  To  investigate  the  conditions  on  which  these  alter- 
natives depend,  let  D  and  D'  be  the  maximum  densities  of  vapour  at 
the  temperatures  t  and  t'  respectively.  Suppose  we  have  tf>t,  and 


376  HYGROMETRY. 

that,  without  altering  the  pressure  }\  the  temperature  of  the  vapour 
is  raised  to  t',  all  contact  with  the  generating  liquid  being  prevented. 
The  vapour  will  no  longer  remain  saturated  ;  but,  on  increasing  the 
pressure  to  /',  keeping  the  temperature  unchanged,  saturation  will 
again  be  produced.  This  latter  change  does  not  alter  the  actual 
quantity  of  vapour,  and  if  we  suppose  its  coefficient  of  expansion  to 
be  the  same  as  that  of  air,  we  shall  have  (§  201) 


D_/  (2) 

D'~/''  1  +  rf' 
and,  by  multiplying  together  equations  (1)  and  (2),  we  have 


V'D'     H/'-/' 

From  this  result  the  following  particular  conclusions  may  be  de- 
duced: — 

1.  If  H//=H//,  VD  =  V'D',  that  is,  the  mass  of  vapour  is  the  same 
in  both  cases;   consequently,  neither  condensation  nor  evaporation 
takes  place. 

2.  If  H'/>  H/,  VD>  V'D',  that  is,  partial  condensation  occurs. 

3.  If  H'/  <H/',  VD  <  V'D',  that  is,  a  fresh  quantity  of  vapour  is 
required  to  maintain  saturation.     In  this  case  the  formula  (1)  can 
only  be  applied  when  we  are  sure  that  there  is  a  sufficient  excess  of 
liquid  to  produce  the  fresh  quantity  of  vapour  which  is  required. 

The  general  formulae  (1),  (2),  (3)  furnish  the  solution  of  many 
particular  problems  which  may  be  proposed  by  selecting  some  one 
of  the  variables  for  the  unknown  quantity. 

298.  Aqueous  Meteors.  —  The  name  meteor,  from  the  Greek  /urewpoc, 
aloft,  though  more  especially  applied  to  the  bright  objects  otherwise 
called  shooting-stars  and  their  like,  likewise  includes  all  the  various 
phenomena  which  have  their  seat  in  the  atmosphere;  for  example, 
clouds,  rain,  and  lightning.  This  use  of  the  word  meteor  is  indeed 
somewhat  rare;  but  the  correlative  term  meteorology  is  invariably 
employed  to  denote  the  science  which  treats  of  these  phenomena,  in 
fact,  the  science  of  matters  pertaining  to  weather. 

By  aqueous  meteors  are  to  be  understood  the  phenomena  which 
result  from  the  condensation  of  -aqueous  vapour  contained  in  the  air, 
such  as  rain,  dew,  and  fog.  This  condensation  may  occur  in  either 
of  two  ways.  Sometimes  it  is  caused  by  the  presence  of  a  cold  body, 
which  reduces  the  film  of  air  in  contact  with  it  to  a  temperature 
below  the  dew-point,  and  thus  produces  the  liquefaction  or  solidifica- 


CLOUD   AND   MIST.  377 

tion  of  a  portion  of  its  vapour  in  the  form  of  dew  or  hoar-frost.  The 
circumstances  connected  with  the  formation  of  dew  will  be  treated 
in  Chapter  xxix.  All  that  we  need  remark  now  is  that  it  essentially 
consists  in  the  deposition  of  moisture  on  the  very  body  whose  low 
temperature  causes  the  condensation. 

When,  on  the  contrary,  the  condensation  of  vapour  takes  place  in 
the  interior  of  a  large  mass  of  air,  the  resulting  liquid  or  solid  falls 
in  obedience  to  gravity.  This  is  the  origin  of  rain  and  snow. 

299.  Cloud  and  Mist. — When  vapour  is  condensed  in  the  midst  of 
the  air,  the  first  product  is  usually  mist  or  cloud,  a  cloud  being 
merely  a  mist  at  a  great  elevation  in  the  air. 

Natural  clouds  are  similar  in  constitution  to  the  cloudy  substance 
which  passes  off  from  the  surface  of  hot  water,  or  which  escapes  in 
puffs  from  the  chimney  of  a  locomotive.  In  common  language  this 
substance  is  often  called  steam  or  vapour,  but  improperly,  for  steam 
is,  like  air,  transparent  and  invisible,  and  the  appearance  in  question 
is  produced  by  the  presence  of  particles  of  liquid  water,  which  have 
been  formed  from  vapour  by  cooling  it  below  its  dew-point. 

Naturalists  are  not  agreed  as  to  the  nature  of  these  particles,  the 
difference  of  opinion  having  arisen  in  the  attempt  to  explain  their 
suspension  in  the  atmosphere.  Some  have  endeavoured  to  account 
for  it  by  maintaining  that  they  are  hollow;1  but  even  if  we  could 
conceive  of  any  causes  likely  to  lead  to  the  formation  of  such  bubbles, 
it  would  furnish  no  solution  of  the  difficulty,  for  the  air  inclosed  in 
a  bubble  is  no  rarer,  but  in  fact  denser,  than  the  external  air  (§  97s); 
the  bubble  and  its  contents  are  therefore  heavier  than  the  air  which 
it  displaces. 

It  is  more  probable  that  the  particles  are  solid  spheres  differing 
only  in  size  from  rain-drops.  It  has  been  urged  against  this  view, 
that  such  drops  ought  to  exhibit  rainbows,  and  the  objection  must 
be  allowed  to  have  some  weight.  The  answer  to  it  is  probably  to 
be  found  in  the  excessive  smallness  of  the  globules.  Indeed,  the  non- 
occurrence  of  bows  may  fairly  be  alleged  as  proving  that  the  dia- 
meters of  the  drops  are  comparable  with  the  lengths  of  waves  of 
light. 

This  smallness  of  the  particles  is  amply  sufficient  to  explain  all  the 
observed  facts  of  cloud  suspension,  without  resorting  to  any  special 
theory.  It  probably  depends  on  the  same  principle  as  the  suspension 

1  Those  who  adopt  this  view  call  them  vesicles  (vesica,  a  bladder),  and  call  mist  or  cloud 
vapour  in  the  vesicular  state. 


378 


HYGROMETKY. 


of  the  motes  which  are  rendered  visible  when  a  beam  of  sunlight 
traverses  a  darkened  room.  It  is  true  that  these  motes,  which  are 
small  particles  of  matter  of  the  most  various  kinds,  are  never  seen 
resting  stationary  in  the  air;  but  neither  are  the  particles  which 
compose  clouds.  All  who  have  ever  found  themselves  in  mountain 
mists  must  have  observed  the  excessive  mobility  of  their  constituent 
parts,  which  yield  to  the  least  breath  of  wind,  and  are  carried  about 
by  it  like  the  finest  dust.  Sometimes,  indeed,  clouds  have  the 
appearance  of  being  fixed  in  shape  and  position ;  but  this  is  an 
illusion  due  to  distance  which  renders  small  movements  invisible. 
In  many  cases,  the  fixity  is  one  of  form  and  not  of  material ;  for 

example,  the  permanent 
cloud  on  a  mountain-top 
often  consists  of  succes- 
sive portions  of  air,  which 
become  cloudy  by  con- 
densation as  they  pass 
through  the  cold  region 
at  the  top  of  the  moun- 
tain, and  recover  their 
transparency  as  they  pass 
away. 

300.  Varieties  of  Cloud. 

— The  cloud  nomenclature  generally  adopted  by  meteorologists  was 
devised  by  Howard,  and  is  contained  in  his  work  on  the  climate  of 

London.  The  fundamen- 
tal forms,  according  to 
him,  are  three — cirrus, 
cumulus,  and  stratus. 

1.  Cirrus  consists  of 
fibrous,  wispy,  or  feathery 
clouds,  occupying  the 
highest  region  of  the  at- 
mosphere. The  name 
mare's-tails,  which  is 
Fig.  274.-cumuiua.  given  them  by  sailors, 

describes      their     aspect 

well.  They  are  higher  than  the  greatest  elevations  attained  by 
balloons,  and  are  probably  composed  of  particles  of  ice.  It  is  in 
this  species  of  cloud,  and  its  derivatives,  that  haloes  are  usually 


Fig.  273.— Cirrus. 


VARIETIES   OF   CLOUD. 


379 


seen ;  and  their  observed  forms  and  dimensions  seem  to  agree  with 
the  supposition  that  they  are  formed  by  refractions  and  reflections 
from  ice- crystals. 

2.  Cumulus  consists  of  rounded  masses,  convex  above  and  com- 
paratively flat  below.     Their  form  bears  a  strong  resemblance  to 
heaps  of  cotton  wool,  hence  the  names  balls  of  cotton  and  wool-packs 
applied  to  these  clouds  by  sailors.     They  are  especially  prevalent  in 
summer,  and  are  probably  formed  by  columns  of  ascending  vapour 
which  become  condensed  at  their  upper  extremities. 

3.  Stratus  consists  of  horizontal  sheets.     Its  situation  is  low  in  the 
atmosphere,  and  its  formation  is  probably  due  to  the  cooling  of  the 

earth  and  the  lower  por- 
tion of  the  air  by  radia- 
tion. It  is  very  frequently 
formed  at  sunset,  and  dis- 
appears at  sunrise. 

Of  the  intermediate 
forms  it  may  suffice  to 
mention  cirro-cumulus, 
which  floats  at  a  higher 
level  than  cumulus,  and 
Fig.  275.— stratus.  consists  usually  of  small 

roundish  masses  disposed 

with  some  degree  of  regularity.  This  is  the  cloud  which  forms  what 
is  known  as  a  mackerel  sky. 

As  a  distinct  form  not  included  in  Howard's  classification,  may  be 

mentioned  scud,  the  char- 
acteristic of  which  is  that, 
from  its  low  elevation,  it 
appears  to  move  with 
excessive  rapidity. 

Howard  gives  the  name 
of  nimbus  to  any  cloud 
which  is  discharging  rain; 
and,  for  no  very  obvious 
reason,  he  regards  this 
rain-cloud  as  compounded 
of  (or  intermediate  be- 
tween) the  three  elementary  types  above  defined. 

The  classification  of  clouds  is  a  subject  which  scarcely  admits  of 


Fig.  276.— Nimbua. 


380  HYGROMETKY. 

precise  treatment;  the  varieties  are  so  endless,  and  they  shade  so 
gradually  into  one  another. 

^  301.  Causes  of  the  Formation  of  Cloud  and  Mist. — Since  clouds  are 
merely  condensed  vapour,  their  formation  is  regulated  by  the  causes 
which  tend  to  convert  vapour  into  liquid.  Such  liquefaction  implies 
the  presence  of  a  quantity  of  vapour  greater  than  that  which,  at  the 
actual  temperature,  would  be  sufficient  for  saturation,  a  condition  of 
things  which  may  be  brought  about  by  the  cooling  of  a  mass  of  moist 
air  in  any  of  the  following  ways : — 

(1.)  By  radiation  from  the  mass  of  air  to  the  cold  sky. 

(2.)  By  the  neighbourhood  of  cold  ground,  for  example,  mountain- 
tops. 

(3.)  By  the  cooling  effect  of  expansion,  when  the  mass  of  air  ascends 
into  regions  of  diminished  pressure.  This  cooling  of  the  ascending 
mass  is  accompanied  by  a  corresponding  warming  of  the  air  which 
descends,  it  may  be  in  some  distant  locality,  to  supply  its  place. 

Causes  (2)  and  (3)  combine  to  produce  the  excessive  rainfall 
which  generally  characterizes  mountainous  districts.1 

It  is  believed  that  waterspouts  are  produced  by  the  rapid  ascent 
of  a  stream  of  air  up  the  axis  of  an  aerial  vortex. 

(4.)  By  the  contact  and  mixture  of  cooler  air.2  It  is  obvious,  how- 
ever, that  this  cooler  air  must  itself  be  warmed  by  the  process ;  and 
as  both  the  temperature  and  vapour-density  of  the  mixture  will  be 
intermediate  between  those  of  the  two  components,  it  does  not  obvi- 
ously follow  (as  is  too  often  hastily  assumed)  that  such  contact  tends 
to  produce  precipitation.  Such  is  however  the  fact,  and  it  depends 
upon  the  principle  that  the  density  of  saturation  increases  faster 
than  the  temperature;  or,  what  is  the  same  thing,  that  the  curve 
in  which  temperature  is  the  abscissa  and  maximum  vapour-density 
the  ordinate,  is  everywhere  concave  upwards. 

It  will  be  sufficient  to  consider  the  case  of  the  mixing  of  two  equal 
volumes  of  saturated  air  at  different  temperatures,  which  we  will 
denote  by  tl  and  £2.  Let  the  ordinates  A  A',  BB'  represent  the 
densities  of  vapour  for  saturation  at  these  temperatures,  A'mB' 
being  the  intermediate  portion  of  the  curve,  and  C  m  the  ordinate 

1  The  rainiest  place  at  present  known  in  Great  Britain  is  about  a  mile  south  of  Sea- 
thwaite  in  Cumberland,  where  the  annual  rainfall  is  about  165  inches.  The  rainiest  place  in 
the  world  is  believed  to  be  Cherra  Ponjee,  in  the  Khasyah  Mountains,  about  300  miles  N.E. 
of  Calcutta,  where  the  annual  fall  is  about  610  inches. 

3  Contact  with  cooler  air  may  be  regarded  as  equivalent  to  mixing :  for  vapour  diffuses 
readily.  . 


FORMATION   OF  CLOUD  AND  MIST.  381 

at  the  middle  point  of  AB,  representing  therefore  the  density  of 
saturation  for  the  temperature  K^i  +  ^)-  When  the  equal  volumes 
are  mixed,  since  the  colder  mass  is 
slightly  the  greater,  the  temperature  of 
the  mixture  will  be  something  less  than 
2(^1 +£a),  and,  if  there  were  no  conden- 
sation of  vapour,  the  density  of  vapour 
-in  the  mixture  would  be  ifAA'+BB') 
=  Cn.  But  the  density  for  saturation 
is  something  less  than  Cm.  The  excess 
of  vapour  is  therefore  represented  by  A  c  B 

something  more  than  mn.     The  amount  Fig.  276 A. 

actually  precipitated  will,  however,  be  less 

than  this,  since  the  portion  which  is  condensed  gives  out  its  latent 
heat,  and  thus  contributes  to  keep  up  the  temperature  of  the 
whole. 

The  cause  here  indicated  combines  with  (3)  to  produce  condensa- 
tion when  masses  of  air  ascend. 

On  the  surface  of  the  earth  mists  are  especially  frequent  in  the 
morning  and  evening;  in  the  latter  case  extending  over  all  the  sur- 
face; in  the  former  principally  over  rivers  and  lakes.  The  mists  of 
evening  are  due  simply  to  the  rapid  cooling  of  the  air  after  the  heat 
of  the  sun  has  been  withdrawn.  In  the  morning  another  cause  is  at 
work.  The  great  specific  heat  of  water  causes  it  to  cool  much  more 
slowly  than  the  air,  so  that  the  vapour  rising  from  a  body  of  water 
enters  into  a  colder  medium,  and  is  there  partly  condensed,  forming 
a  mist,  which,  however,  confines  itself  to  the  vicinity  of  the  water, 
and  is  soon  dissipated  by  the  heat  of  the  rising  sun. 
^  302.  Rain. — In  what  we  have  stated  regarding  the  constitution  of 
clouds,  it  is  implied  that  clouds  are  always  raining,  since  the  drops 
of  which  they  are  composed  always  tend  to  obey  the  action  of  gravity. 
But,  inasmuch  as  there  is  usually  a  non-saturated  region  intervening 
between  the  clouds  and  the  surface  of  the  earth,  these  drops,  when 
very  small,  are  usually  evaporated  before  they  have  time  to  reach 
the  ground.  Ordinary  rain-drops  are  formed  by  the  coalescing  of  a 
number  of  these  smaller  particles. 

By  the  amount  of  annual  rainfall  at  a  given  place  is  meant  the 
depth  of  water  that  would  be  obtained  if  all  the  rain  which  falls 
there  in  a  year  were  collected  into  one  horizontal  sheet;  and  the 
depth  of  rain  that  falls  in  any  given  shower  is  similarly  reckoned. 


382  HYGROMETRY. 

It  is  the  depth  of  the  pool  which  would  be  formed  if  the  ground 
were  perfectly  horizontal,  and  none  of  the  water  could  get  away. 
The  instrument  employed  for  determining  it  is  called  a  rain-gauge. 
It  has  various  forms,  one  of  which  is  represented  in 
the  adjoining  figure.  B  is  a  funnel  into  which  the 
rain  falls,  and  from  which  it  trickles  into  the  reservoir 
A.  It  is  drawn  off  by  means  of  the  stop-cock  r,  and 
measured  in  a  graduated  glass,  each  division  of  which 
corresponds  to  T^-$  of  an  inch  of  rain.1 

It  is  essential  that  the  receiving  surface — the  top  of 
the  funnel — should  be  truly  horizontal,  otherwise  the 
gauge  will  catch  too  much  or  too  little  according  to 
the  direction  of  the  wind. 

The  best  place  for  a  rain-gauge  is  the  centre  of  a 
level  and  open  plot ;  and  the  height  of  its  receiving 
surface  should  be  not  less  than  6  inches,  to  avoid  in- 
splashing.  The  roof  of  a  house  is  a  bad  place  on  ac- 
count of  the  eddies  which  abound  there. 

A  circumstance  which  has  not  yet  been  fully  explained  is  that  the 
higher  a  gauge  is  above  the  ground  the  less  rain  it  catches.  In  the 
case  of  gauges  on  the  top  of  poles  in  an  open  situation,  the  amount 
collected  is  diminished  by  -y-^ih  part  of  itself  by  doubling  the  height 
of  the  receiving  surface,  as  shown  by  comparing  gauges  in  the  same 
plot  of  ground  at  heights  ranging  from  6  inches  to  20  feet.2 

By  means  of  tipping-buckets  and  other  arrangements,  automatic 
records  of  rainfall  are  obtained  at  the  principal  observatories.  The 
best  of  these  pluviometers  is  Osier's,  which,  by  means  of  spiral 
springs  stretched  by  the  weight  of  the  water,  furnishes  a  continuous 
record,  until  a  quarter  of  an  inch  has  been  collected,  when  the 
reservoir  empties  itself,  and  a  fresh  record  begins. 

The  mean  annual  rainfall,  according  to  Mr.  Symons,  is  20  inches  at 
Lincoln  and  Stamford;  21  at  Aylesbury,  Bedford,  and  With  am;  24  at 
London  and  Edinburgh  ;  30  at  Dublin,  Perth,  arid  Salisbury ;  33  at 
Exeter  and  Clifton ;  35  to  36  at  Liverpool  and  Manchester ;  40  at 
Glasgow  and  Cork;  50  at  Gal  way;  64  at  Greenock  and  Inverary;  86 
at  Dartmoor;  and  91  on  Benlomond. 

1  The  best  work  on  the  subject  of  rain  and  its  measurement  is  the  little  treatise  entitled 
Rain  by  Mr.  G.  J.  Symons,  a  gentleman  who  devotes  his  life  to  the  investigation  of 
British  rainfall.  Mr.  Symons  would  probably  tell  us  that  the  funnel  in  the  above  figure 
is  too  flat,  and  would  cause  some  of  the  rain  to  splash  out. 

8  This  appears  from  the  table  in  Symons  on  Rain,  p.  19. 


SNOW    AND    HAIL.  383 

303.  Snow  and  Hail. — Snow  is  probably  formed  by  the  direct  pas- 
sage of  vapour  into  the  solid  state.  Snow-flakes,  when  examined 
under  the  microscope,  are  always  found  to  be  made  up  of  elements 
possessing  hexagonal  symmetry.  In  Fig.  278  are  depicted  various 
forms  observed  by  Captain  Scoresby  during  a  long  sojourn  in  the 
Arctic  regions. 

In  these  cold  countries  the  air  is  often  filled  with  small  crystals  of 
ice  which  give  rise  to  the  phenomena  of  haloes  and  parhelia. 

Hail  is  probably  due  to  the  freezing  of  rain-drops  in  their  passage 
through  strata  of  air  colder  than  those  in  which  they  were  formed. 
Even  in  fine  summer  weather,  a  freezing  temperature  exists  at  the 
height  of  from  1 0,000  to  20,000  feet,  and  it  is  no  unusual  thing  for 
a  colder  stratum  to  underlie  a  wTarmer,  although,  as  a  general  rule, 
the  temperature  diminishes  in  ascending. 


Fig.  278.— Snow-crystals. 


CHAPTER    XXIX. 


RADIANT  HEAT. 


\ 


305.  Radiation. — When  two  bodies  at  different  temperatures  are 
brought  opposite  to  each  other,  an  unequal  exchange  of  heat  takes 
place  through  the  intervening  distance ;  the  temperature  of  the  hotter 
body  falls,  while  that  of  the  colder  rises,  and  after  some  time  the 
temperature  of  both  becomes  the  same.  This  propagation  of  heat 
across  an  intervening  space  is  what  is  meant  by  radiation,  and  the 
heat  transmitted  under  these  conditions  is  called 
radiant  heat.  Instances  of  heat  communicated  by 
radiation  are  the  heat  of  a  fire  received  by  a  person 
sitting  in  front  of  it,  and  the  heat  which  the  earth 
receives  from  the  sun. 

This  last  instance  shows  us  that  radiation  as  a 
means  of  propagating  heat  is  independent  of  any 
ponderable  medium.  But  since  the  solar  heat  is 
accompanied  by  light,  it  might  still  be  questioned 
whether  dark  heat  could  in  the  same  way  be  propa- 
gated through  a  vacuum. 

This  was  tested  by  Rumford  in  the  following 
way: — He  constructed  a  barometer  (Fig.  279),  the 
upper  part  of  which  was  expanded  into  a  globe, 
and  contained  a  thermometer  hermetically  sealed 
into  a  hole  at  the  top  of  the  globe,  so  that  the  bulb 
of  the  thermometer  was  at  the  centre  of  the  globe. 
The  globe  was  thus  a  Torricellian  vacuum-chamber. 
By  melting  the  tube  with  a  blow-pipe,  the  globe 
was  separated,  and  was  then  immersed  in  a  vessel 
containing  hot  water,  when  the  thermometer  was  immediately 
observed  to  rise  to  a  temperature  evidently  higher  than  could  be 

25 


Fig.  279.— Rumford'a 
Experiment. 


386  RADIANT   HEAT. 

due  to  the  conduction  of  heat  through  the  stem.  The  heat  had  there- 
fore been  communicated  by  direct  radiation  through  the  vacuum 
between  the  sides  of  the  globe  and  the  bulb  a  of  the  thermometer. 

306.  Radiant  Heat  travels  in  Straight  Lines. — Inja,  uniform  medium 
the  radiation  of  heat  takes  place  in  straight  lines.     If,  for  instance, 
between  a  thermometer  and  a  source  of  heat,  there  be  placed  a  num- 
ber of  screens,  each  pierced  with  a  hole,  and  if  the  screens  be  so 
arranged  that  a  straight  line  can  be  drawn  without  interruption  from 
the  source  to  the  thermometer,  the  temperature  of  the  latter  imme- 
diately rises;    if  a  different  arrangement  be  adopted,   the  heat  is 
stopped  by  the  screens,  and  the  thermometer  indicates  no  effect. 

The  heat  which  travels  along  any  one  straight  line  is  called  a  ray 
of  heat.  Thus  we  say  that  rays  of  heat  issue  from  all  points  of  the 
surface  of  a  heated  body,  or  that  such  a  body  emits  rays  of  heat. 

Such  language  may  be  thought  to  imply  the  hypothesis  that  heat 
is  a  substance  (caloric)  which  is  accumulated  in  bodies,  and  emitted 
by  them  in  all  directions.  A  ray  of  heat  would  thus  consist  of  a 
series  of  molecules  of  caloric  issuing  forth  one  after  the  other  in  a 
straight  line.  But,  in  fact,  the  definition  which  we  have  just  given 
of  a  ray  of  heat  is  independent  of  any  hypothesis,  and  is  simply 
experimental;  it  amounts  merely  to  the  expression  of  the  incontest- 
able fact  that  the  direction  of  radiation  is  rectilinear.  Whatever 
idea  we  may  form  about  the  nature  of  heat,  it  must  be  such  as  to 
imply  this  rectilinear  propagation. 

It  is  now  generally  admitted  that  both  heat  and  light  are  due  to 
a  vibratory  motion  which  is  transmitted  through  space  by  means  of 
a  fluid  called  ether.  According  to  this  theory  the  rays  of  light  and 
heat  are  lines  drawn  in  all  directions  from  the  origin  of  motion,  and 
along  which  the  vibratory  movement  advances. 

307.  Law  of  Cooling. — It  is  often  important  to  know  the  law 
according  to  which  a  body  cools  when  placed  in  an  inclosure  of  lower 
temperature  than  its  own;  for  we  are  thus  enabled  to  take  account 
of  the  heat  which  a  body  loses  during  the  progress  of  an  experiment 
This  law,  when  stated  in  such  terms  as  to  be  applicable  to  all  possible 
differences  of  temperature  and  all  possible  conditions  of  the  surround- 
ing medium,  becomes  exceedingly  complex;  but  when  the  difference 
of  temperature  is  small,  amounting  only  to  a  few  degrees,  the  law 
known  as  Newton's  law  of  cooling  can  be  applied  without  sensible 
error.     It  is  this: — the  rate  at  which  the  body  loses  heat  is  propor- 
tional to  the  difference  between  the  temperature  of  its  surface  and 


LAW   OF   COOLING.  387 

that  of  the  inclosure.  If  the  body  be  of  sensibly  uniform  tempera- 
ture throughout  its  whole  mass,  as  in  the  case  of  a  vessel  with  thin 
metallic  sides  containing  water  which  is  kept  stirred,  or  of  the  quick- 
silver in  the  bulb  of  a  thermometer,  the  fall  of  temperature  is  pro- 
portional to  the  loss  of  heat,  and  Newton's  law  as  applied  to  such  a 
body  asserts  that  the  rate  at  which  the  temperature  falls  is  propor- 
tional to  the  excess  of  the  temperature  of  the  body  above  that  of  the 
inclosure. 

To  test  this  law  experimentally,  we  observe  from  time  to  time  the 
excess  of  the  temperature  of  a  thermometer  above  that  of  the  air  in 
which  it  is  cooling.  It  is  found,  that,  if  the  observations  are  made 
at  equal  intervals  of  time,  the  observed  excesses  form  a  decreasing 
geometric  series. 

To  express  this  fact  algebraically,  let  60  clenote  the  initial  excess  of 

temperature,  and  ^  the  ratio  of  the  series.  Then  the  excess  at  the 
end  of  a  unit  of  time  will  be  -^  at  the  end  of  two  units  -f.  and  after 

m  mz> 

t  units  -2;  so  that  if  6  denote  the  excess  at  time  t,  we  have 

»-!t.».*H.  (1) 

One  pair  of  observations  is  sufficient  to  determine  the  value  of  the 
constant  m,  which  is  different  for  different  thermometers. 

By  rate  of  cooling  is  meant  the  fall  of  temperature  per  unit  time 
which  is  taking  place  at  the  instant  considered.  This  is  computed 
approximately  by  dividing  the  fall  of  temperature  in  a  small  interval 
of  time  by  the  length  of  the  interval.  Its  exact  value  is  given  by 
the  differential  calculus,  and  is 

-  ~  =  00™-'  loge  m  =  6  loge  m,  (2) 

which  is  proportional  to  0,  as  asserted  by  Newton's  law 

A  precisely  similar  law  holds  for  warming. 

307 A.  Cooling  by  Radiation  in  Vacuo. — The  cooling  of  a  thermo- 
meter in  air  is  effected  partly  by  the  contact  of  the  air,  and  partly 
by  radiation.  When  the  thermometer  is  placed  in  the  centre  of  a 
vacuous  space,  radiation  alone  can  operate,  namely,  radiation  from 
the  thermometer  to  the  walls  of  the  inclosure.  The  law  of  cooling 
under  these  conditions  has  been  investigated  experimentally  by 
Dulong  and  Petit,  and  was  reduced  by  them  to  a  formula  which  was 
found  to  be  accurate  within  the  limits  of  experimental  error  for  all 


388  RADIANT  HEAT. 

the  ranges  of  temperature  employed,  the  excess  of  the  temperature 
of  the  thermometer  above  that  of  the  walls  of  the  inclosure  ranging 
from  20°  to  240°  C.  They  found  that  the  rate  of  cooling  did  not 
depend  upon  the  difference  of  temperature  alone,  but  was  faster  at 
high  than  at  low  temperatures ;  also  that,  for  a  given  temperature  of 
the  walls,  the  rate  of  cooling  was  not  simply  proportional  to  the 
excess,  but  increased  more  rapidly.  Both  these  results  are  expressed 
by  their  formula 

V=ca«  («'-l),  (3) 

where  V  denotes  the  rate  of  cooling,  c  and  a  constants,  t  the  tem- 
perature of  the  walls  of  the  inclosure,  and  0  the  excess  of  temperature, 
so  that  t  +  0  is  the  temperature  of  the  thermometer.  If  we  denote 
this  by  t'  the  formula  may  be  thrown  into  the  more  symmetrical 

form 

V=c(a*-a«),  (4) 

which  suggests  the  idea  that  an  unequal  exchange  of  heat  takes  place 
between  the  thermometer  and  the  walls,  the  thermometer  giving  to 
the  walls  a  quantity  of  heat  represented  by  a*',  and  receiving  in 
exchange1  only  the  quantity  a*.  The  former  of  these  amounts 
remains  the  same  at  all  temperatures  of  the  inclosure,  and  the  latter 
is  the  same  for  all  temperatures  of  the  thermometer. 

When  the  temperatures  are  Centigrade,  the  constant  a  is  TOOTT. 
When  they  are  Fahrenheit  it  is  1-0043,  the  form  of  the  expression 
for  V  being  unaffected  by  a  change  of  the  zero  from  which  the  tem- 
peratures are  reckoned.  The  value  of  c  depends  upon  the  size  of  the 
bulb  and  some  other  circumstances,  and  is  changed  by  a  change  of 
zero. 

By  developing  a?  in  ascending  powers  of  0,  it  will  be  found  that 
formula  (3)  agrees  sensibly  with  Newton's  law  when  the  excess  of 
temperature  does  not  exceed  a  few  degrees. 

308.  Law  of  Inverse  Squares. — If  we  take  a  delicate  thermometer 
and  place  it  at  successively  increasing  distances  from  a  source  of  heat, 
the  temperature  indicated  by  the  instrument  will  exceed  that  of  the 
atmosphere  by  decreasing  amounts,  showing  that  the  intensity  of 
radiant  heat  diminishes  as  the  distance  increases.  The  law  of  varia- 

1  According  to  the  theory  of  exchanges,  the  heat  emitted  by  the  thermometer  is  cat'  plus 
a  constant  term  depending  on  the  zero  of  the  temperature  scale  employed,  and  the  heat 
absorbed  by  it  is  cat  plus  the  same  constant.  It  may  be  remarked  that  the  factor  c  also 
depends  upon  the  zero  from  which  temperatures  are  reckoned  as  well  as  upon  the  length 
of  the  degrees,  whereas  a  depends  on  the  latter  only. 


LAW  OF  INVERSE  SQUARES.  389 

fcion  may  be  discovered  by  experiment.  In  fact,  when  the  excess  of 
temperature  of  the  thermometer  becomes  fixed,  we  know  that  the 
heat  received  is  equal  to  that  lost  by  radiation ;  but  this  latter  is,  by 
Newton's  law,  proportional  to  the  excess  of  temperature  above  that 
of  the  surrounding  air;  we  may  accordingly  consider  this  excess  as 
the  measure  of  the  heat  received.  It  has  been  found,  by  experiments 
at  different  distances,1  that  the  excess  is  inversely  proportional  to  the 
square  of  the  distance ;  we  may  therefore  conclude  that  the  intensity 
of  the  heat  received  from  any  source  of  heat  varies  inversely  as  the 
square  of  the  distance. 

The  following  experiment,  devised  by  Tyndall,  supplies  another 
simple  proof  of  this  fundamental  law : — 

The  thermometer  employed  is  a  Melloni's  pile,  the  nature  of  which 
we  shall  explain  in  §  313.  This  is  placed  at  the  small  end  of  a  hollow 
cone,  blackened  inside,  so  as  to  prevent  any  reflection  of  heat  from 
its  inner  surface.  The  pile  is  placed  at  S  and  S'  in  front  of  a  vessel 


Fig.  280.— Law  of  Inverse  Squares. 

filled  with  boiling  water,  and  coated  with  lamp-black  on  the  side 
next  the  pile.  It  will  now  be  observed  that  the  temperature 
indicated  by  the  pile  remains  constant  for  all  distances.  This  result 
proves  the  law  of  inverse  squares.  For  the  arrangement  adopted 
prevents  the  pile  from  receiving  more  heat  than  that  due  to  the  area 
of  A B  in  the  first  case,  and  to  the  area  A'B'  in  the  second.  These 
are  the  areas  of  two  circles,  whose  radii  are  respectively  proportional 
to  SO  and  S'O;  and  the  areas  are  consequently  proportional  to  the 

1  The  dimensions  of  the  source  of  heat  must  be  small  in  comparison  with  the  distance  of 
the  thermometer,  as  otherwise  the  distances  of  different  parts  of  the  source  of  heat  from 
the  thermometer  are  sensibly  different.  In  this  case,  the  amount  of  heat  received  varies 
directly  as  the  solid  angle  subtended  by  the  source  of  heat. 


390  RADIANT  HEAT. 

squares  of  SO  and  S'O.  Since,  therefore,  these  two  areas  communi- 
cate the  same  quantity  of  heat  to  the  pile,  the  intensity  of  radiation 
must  vary  inversely  as  the  squares  of  the  distances  S  O  and  S'  O. 

The  law  of  inverse  squares  may  also  be  established  a  priori  in  the 
following  manner: — 

Suppose  a  sphere  of  given  radius  to  be  described  about  a  radiating 
particle  as  centre.  The  total  heat  emitted  by  the  particle  will  be 
received  by  the  sphere,  and  all  points  on  the  sphere  will  experience 
the  same  calorific  effect  If  now  the  radius  of  the  sphere  be  doubled, 
the  surface  will  be  quadrupled,  but  the  total  amount  of  heat  remains 
the  same  as  before,  namely,  that  emitted  by  the  radiating  particle. 
Hence  we  conclude  that  the  quantity  of  heat  absorbed  by  a  given 
area  on  the  surface  of  the  large  sphere  is  one-fourth  of  that  absorbed 
by  an  equal  area  on  the  small  sphere;  which  agrees  with  the  law 
stated  above. 

This  demonstration  is  valid,  whether  we  suppose  the  radiation  of 
heat  to  consist  in  the  emission  of  matter  or  in  the  emission  of  energy ; 
for  energy  as  well  as  matter  is  indestructible,  and  remains  unaltered 
in  amount  during  its  propagation  through  space. 

309.  Law  of  the  Reflection  of  Heat. — When  a  ray  of  heat  strikes 
a  polished  surface,  it  is  reflected  in  a  direction  determined  by  fixed 
laws. 

If  at  the  point  of  incidence,  that  is,  the  point  where  the  ray  meets 
the  surface,  a  line  be  drawn  normal  or  perpendicular  to  the  surface, 
the  plane  passing  through  this  line  and  the  incident  ray  is  called  the 
plane  of  incidence.  With  this  explanation  we  proceed  to  give  the 
laws  of  the  reflection  of  heat: — 

1.  When  a  ray  of  heat  is  reflected  by  a  surface,  the  line  of  reflec- 
tion lies  in  the  plane  of  incidence. 

2.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence ;  that 
is,  the  reflected   and   incident   rays  make  equal  angles  with  the 
normal  to  the  surface  at  the  point  of  incidence. 

We  shall  see  hereafter  that  these  laws  are  precisely  the  same  as 
those  of  the  reflection  of  light.  In  the  case  of  light,  they  can  be  very 
strictly  verified.  And  since,  in  all  phenomena  involving  at  once 
heat  and  light,  we  find  the  same  laws  holding  for  calorific  as  for 
luminous  rays,  we  may  consider  the  demonstration  of  these  laws  in 
the  case  of  light  as  sufficient  to  prove  that  they  hold  good  for  rays 
of  heat  also. 

310.  Burning-mirrors. — The  laws  of  the  reflection  of  heat,  however, 


BURNING-MIRRORS.  391 

may  be  directly  verified  by  some  well-known  experiments,  especially 
by  means  of  a  concave  spherical  mirror  (Fig.  281),  that  is,  a  mirror 
consisting  of  a  portion  of  a  hollow  sphere,  with  its  concave  side 
polished.  The  principal  axis  of  this  mirror  is  a  line  CF  passing 
through  the  centre  of  the  sphere,  and  through  the  middle  point  A 
(which  may  be  called  the  pole)  of  the  mirror  itself.  It  may  easily 
be  deduced  from  the  law  of  reflection  that  if  a  pencil  of  rays  parallel 
to  the  axis  are  incident  upon  the  mirror,  they  will  all,  after  reflection, 
pass  through  or  very  near  the  point  F  which  bisects  the  radius,  and 


Fig.  281.— Focus  of  Concaye  Mirror. 

is  called  the  principal  focus.  We  may  remark  that  the  rays  need  not 
be  parallel  to  the  principal  axis;  it  is  only  necessary  that  they  be 
parallel  to  each  other,  in  order  that  they,  should  meet  in  a  focus  situ- 
ated on  the  line  drawn  through  the  centre  in  a  direction  parallel  to 
the  pencil  of  rays. 

These  theoretical  conclusions  have  been  verified  by  experiments 
with  burning-mirrors.  These  are  spherical1  concave  mirrors,  turning 
about  an  axis,  so  as  to  receive  the  rays  of  the  sun  perpendicularly 
upon  their  surface.  The  heat  produced  under  these  circumstances  at 
the  focus  of  the  mirror,  is  sufficiently  great  to  inflame  any  combus- 
tible material  placed  there,  or  even  to  produce  more  striking  effects. 
Tschirnhausen's  mirror,  for  instance,  which  was  constructed  in  1G87, 
and  was  about  6  J  feet  in  diameter,  was  able  to  melt  copper  or  silver, 
and  to  vitrify  brick.  Instead  of  curved  mirrors,  Buffon  employed  a 

1  Parabolic  mirrors  are  perhaps  more  frequently  employed  for  experiments  on  the  reflec- 
tion of  heat.  All  rays  falling  on  a  parabolic  mirror  parallel  to  its  axis  are  accurately 
reflected  to  its  focus,  and  all  rays  incident  upon  it  from  a  source  of  heat  or  light  at  the 
focus  are  reflected  parallel  to  the  axis. 

The  mirrors  in  the  experiment  of  §  311  are  most  easily  adjusted  by  first  placing  a  source 
of  light  (such  as  the  flame  of  a  candle)  in  one  focus,  and  forming  a  luminous  image  in  the 
other.  We  have  thus  a  convincing  proof  that  heat  and  light  obey  the  same  laws  as  regards 
direction  of  reflection. 


392 


RADIANT  HEAT. 


number  of  movable  plane  mirrors,  which  were  arranged  so  that  the 
different  pencils  of  heat-rays  reflected  by  them  converged  to  nearly 

the  same  focus.  In  this  way  he 
obtained  an  extremely  powerful 
effect,  and  was  able,  for  instance, 
to  set  wood  on  fire  at  a  distance 
of  between  80  and  90  yards. 
This  is  the  method  which  Archi- 
medes is  said  to  have  employed 
for  the  destruction  of  the  Roman 
fleet  in  the  siege  of  Syracuse; 
and  though  the  truth  of  the  story 
is  considered  doubtful,  it  is  not 
altogether  absurd. 

311.  Conjugate  Mirrors.  —  A 
more  rigorous  demonstration  of 
the  laws  of  the  reflection  of  heat 
is  afforded  by  the  celebrated  ex- 
periment of  the  conjugate  mir- 
rors, which  is  generally  ascribed 
to  Pictet  of  Geneva. 

Two  spherical  mirrors  are  plac- 
ed at  &ny  convenient  distance, 
with  their  concave  surfaces  to- 
wards each  other  and  their  axes  in  the  same  straight  line.  In  the 
focus  of  one  of  them  is  placed  a  small  furnace,  or  a  red-hot  cannon- 
ball,  and  In  the  focus  of  the  other  some  highly  inflammable  mate- 
rial, such  as  phosphorus  or  gun-cotton.  On  exciting  the  furnace 
with  bellows,  the  substance  in  the  other  focus  immediately  takes 
fire.  With  two  mirrors  of  14  inches  diameter,  gun-cotton  may  thus 
be  set  on  fire  at  a  distance  of  more  than  30  feet.  The  explanation 
is  very  easy.  The  rays  of  heat  coming  from  the  focus  of  the  first 
mirror  are  reflected  in  parallel  lines,  and,  on  impinging  upon  the 
surface  of  the  second  mirror,  converge  again  to  its  focus,  and  are 
thus  concentrated  upon  the  inflammable  material  placed  there. 

It  might  appear  at  first  sight  that  the  experiment  is  not  very  pre- 
cise, owing  to  the  comparatively  large  size  of  the  source  of  heat;  but 
we  must  remark  that  only  a  very  small  portion  of  this  actually  pro- 
duces any  effect;  the  rest  serving  merely  to  maintain  a  sufficiently 
high  temperature  at  the  points  which  reallv  send  rays  to  the  focus. 


Fig.  282. — Burning  Mirror. 


CONJUGATE  MIRRORS. 


393 


Again,  the  image  of  the  source  of  heat  which  is  formed  at  the  focus 
of  the  second  mirror,  is  so  small,  that  the  slightest  change  in  the 
position  of  either  mirror  causes  the  failure  of  the  experiment.  Great 


Fig.  283.— Conjugate  Mirrors. 

exactness  is  therefore  required  to  insure  success;  and  we  may  con- 
sequently regard  the  experiment  as  a  tolerably  severe  test  of  the 
truth  of  the  laws  of  reflection  which  have  been  quoted  above. 
*{  312.  Different  Properties  of  Bodies  with  respect  to  Radiant  Heat.— 
Suppose  a  quantity  of  heat  denoted  by  unity  to  be  incident  upon 
the  surface  of  a  body.  This  quantity  will  be  divided  into  several 
distinct  parts. 

1.  A  portion  will  be  regularly  reflected  according  to  the  law  given 

above.     If  the  fraction  of  heat  thus  reflected  be  denoted  by  p  then 
-  is  the  measure  of  the  reflecting  power. 

2.  A  portion  -^  will  be  irregularly  reflected,  and  will  be  scattered 

or  diffused  through  space  in  all  directions.     Thus  -r  is  the  measure 
of  the  diffusive  power. 

3.  A  portion  -  will  penetrate  into  the  body  so  as  to  be  absorbed 

by  it,  and  to  contribute  to  raise  its  temperature ;  —  is  therefore  the 
measure  of  the  absorbing  power. 


394  RADIANT  HEAT. 

4.  Finally,  we  shall  have,  in  many  cases,  a  fourth  portion  i  which 

passes  through  the  body  without  contributing  to  raise  its  tempera- 
ture. This  fraction,  which  exists  only  in  the  case  of  diathermanous 
bodies,  is  the  measure  of  diathermancy  or  transmissive  power. 

The  sum  of  these  fractional  parts  must  evidently  make  up  the 
original  unit  ;  that  is 

1  +  1+1+1=1. 

r      d      a      d 

312  A.  Relation  between  Absorption  and  Emission.  —  A  different  mode 
of  expressing  absorbing  power  is  sometimes  required  —  a  mode  which 
shall  express  the  rate  at  which  the  body  gains  heat  when  completely 
inclosed  in  an  exhausted  space  whose  walls  have  a  higher  tempera- 
ture than  its  own. 

Let  the  walls  be  covered  with  lamp-black,  and  have  a  small  excess 
of  temperature  0,  and  let  the  area  of  the  body's  surface  (which  must 
have  no  concavities)  be  S  ;  then  the  rate  at  which  the  body  gains 
heat  is  proportional  to  SO,  and  may  be  denoted  by  AS0,  A  being  a 
coefficient  which  is  independent  of  6  provided  that  d  is  small,  but 
which  is  not  necessarily  the  same  at  high  as  at  low  temperatures 
We  shall  call  this  factor  A  the  coefficient  of  absorption;  and  the  heat 
gained  by  the  body  in  a  short  interval  of  time  r  will  be 


If  now  we  suppose  the  inclosed  body  to  be  warmer  than  the  walls 
by  a  small  excess  0',  the  rate  of  losing  heat  will  be  proportional  to 
SO',  and  may  be  denoted  by  ES0',  E  being  called  the  coefficient  of 
emission  ;  and  the  quantity  of  heat  lost  by  the  body  in  the  short 
time  r  is 


Now  experiment  shows  that,  for  any  given  body  at  a  given  tempera- 
ture, the  values  of  A  and  E  are  equal  ;  for  example,  a  thermometer 
inclosed  in  a  vacuous  globe,  as  in  the  experiments  of  Dulong  and 
Petit  (§  307  A),  takes  the  same  time  to  rise  1°  as  to  fall  1°  if  the  initial 
difference  of  temperature  between  the  thermometer  and  the  globe 
was  2°  in  each  case. 

The  coefficient  of  emission  then,  at  any  given  temperature,  is  equal 
to  the  coefficient  of  absorption;  and  we  may  therefore  give  it  a  sym- 
metrical name,  and  call  it  the  coefficient  of  radiation.  A  substance 
for  which  this  coefficient  has  a  large  value  is  said  to  be  a  good  radiator. 

Now  it  is  obviously  impossible  for  a  body  to  absorb  more  heat 


ABSORPTION  AND   EMISSION.  395 

than  falls  upon  it.  There  must  therefore  be  a  limiting  value  of  A 
applicable  to  a  body  whose  absorbing  power  —  is  unity;  and  the  same 
limiting  value  must  exist  for  E  which  is  equal  to  A. 

Hence  it  appears  that  good  radiation  depends  rather  upon  defect 
of  resistance  than  upon  any  positive  power.  A  perfect  radiator  would 
be  a  substance  whose  surface  opposed  no  resistance  to  the  communi- 
cation of  radiant  heat  in  either  direction;  while  an  imperfect  radiator 
is  one  whose  surface  allows  a  portion  to  be  communicated  through  it, 
and  reflects  another  portion  regularly  or  irregularly. 

We  may  conveniently  employ  —  to  denote  the  ratio  of  the  heat 

emitted  by  a  surface  to  that  which  would  be  emitted  by  a  perfect 
radiator  at  the  same  temperature.  We  can  then  assert  that  for  any 
one  kind  of  heat 

1=1 

e      a' 

or  the  emissive  and  absorptive  powers  are  equal. 

The  reflecting  and  diffusive  powers  of  lamp-black  are  so  insigni- 
ficant, at  temperatures  below  100°  C.,  that  this  substance  is  com- 
monly adopted  as  the  type  of  a  perfect  radiator,  and  the  emissive 
and  absorptive  powers  of  other  substances  are  usually  expressed  by 
comparison  with  it. 

Recent  experiments  by  Sir  W.  Thomson  show  that  the  coefficient 
of  radiation  A  or  E  between  two  lamp-black  surfaces  radiating  to 
each  other  in  vacuo  is  about  •&$&&>  3  being  expressed  in  gramme- 
degrees  (§  339),  0  in  degrees,1  S  in  square  centimetres  of  surface  of 
the  inclosed  body,  and  r  in  seconds. 

312 B.  Different  Kinds  of  Heat-rays. — A  beam  of  radiant  heat  or 
light  is  not,  generally  speaking,  homogeneous,  but  (as  we  shall  more 
fully  explain  in  connection  with  optics)  is  made  up  of  rays  differing 
in  wave-length,  and  capable  of  being  separated  by  transmission 
through  a  prism,  those  which  have  the  shortest  wave-lengths  being 
refracted  or  turned  out  of  their  original  direction  to  the  greatest 
extent.  A  beam  of  radiant  heat  or  light  may  also  possess  peculiar 
properties  comprehended  under  the  name  of  polarization. 

1  It  is  immaterial  whether  the  Cent,  or  Fahr.  scale  be  employed — for  the  degree  and 
gramme-degree  change  in  the  same  ratio. 

The  experiments  referred  to  (which  will  shortly  be  published  in  the  Proc.  Roy.  Soc.), 
were  conducted  by  observing  the  cooling  of  a  copper  ball  in  an  inclosure  filled  with  air. 
The  total  loss  of  heat  corresponded  to  a  co-efficient  i^nnr*  and  it  was  estimated  that  half  the 
loss  was  due  to  atmospheric  contact,  and  the  other  half  to  radiation. 


S96  RADIANT  HEAT. 

Almost  all  substances  exhibit  the  phenomenon  of  selective  absorp- 
tion, that  is  to  say,  they  absorb  some  kinds  of  heat  more  readily 
than  others ;  and  it  has  been  completely  established  by  a  variety  of 
experiments,  that  the  heat  which  a  body  emits  when  radiating  to 
bodies  colder  than  itself,  consists  chiefly  of  the  same  elementary  heat- 
rays  which  it  absorbs  most  copiously  from  bodies  hotter  than  itself. 

312  c.  Theory  of  Exchanges. — Many  of  the  phenomena  of  radiation 
are  most  simply  explained  by  the  view  now  usually  called  the  theory 
of  exchanges,  but  originally  promulgated  by  Prevost  of  Geneva  under 
the  name  of  the  theory  of  mobile  equilibrium  of  temperature.  This 
theory  asserts  that  all  bodies  are  constantly  giving  out  radiant  heat, 
at  a  rate  depending  upon  their  substance  and  temperature,  but 
independent  of  the  substance  or  temperature  of  the  bodies  which 
surround  them  j1  and  that,  when  a  body  is  kept  at  a  uniform  tem- 
perature, it  receives  back  just  as  much  heat  as  it  gives  out. 

According  to  this  view,  two  bodies  at  the  same  temperature, 
exposed  to  mutual  radiation,  exchange  equal  amounts  of  heat;  but  if 
two  bodies  have  unequal  temperatures,  that  which  is  at  the  higher 
temperature  gives  to  the  other  more  than  it  receives  in  exchange. 

As  a  necessary  accompaniment  of  this  view,  it  is  maintained  that, 
for  each  particular  kind  of  heat,  the  emissive  and  absorbing  powers 

-  and  —  (§  312  A)  are  equal  for  any  one  body,  and  at  any  given  tempera- 
ture; this  inference  being  drawn  from  the  well-known  experimental 
fact  that  a  body  completely  surrounded  by  an  inclosure  whose  walls 
are  preserved  at  a  constant  temperature,  will  ultimately  take  that 
temperature.  For  the  details  of  the  reasoning  we  must  refer  to 
special  treatises.2 

According  to  this  theory,  the  coefficient  A  or  E  (§  312  A)  for  a  body 
at  temperature  t°,  represents  the  difference  between  the  absolute 
emission  at  this  temperature  and  at  the  temperature  £°  +  l0. 

313.  Thermoscopic  Apparatus  employed  in  Researches  connected 
with  Radiant  Heat. — An  indispensable  requisite  for  the  successful 
study  of  radiant  heat  is  an  exceedingly  delicate  thermometer.  For 
this  purpose  Leslie,  about  the  beginning  of  the  present  century, 
invented  the  differential  thermometer,  with  which  he  conducted  some 
very  important  investigations,  the  main  results  of  which  are  still 
acknowledged  to  be  correct.  Modern  investigators,  as  Melloni, 

1  See  §  307  A,  formula  (4)  and  foot-note. 

2  Report  on  the  Theory  of  Exchanges  by  Balfour  Stewart,  in  British  Association  Report, 
1861,  p.  97;  and  Stewart  on  Heat,  book  ii.  chap.  iii. 


THERMOSCOPIC   APPARATUS. 


397 


Laprovostaye,  &c.,  have  exclusively  employed  Nobili's  thermo-multi- 
plier,  which  is  an  instrument  of  much  greater  delicacy  than  the 
differential  thermometer. 

The  thermo-pile  inverted  by  Nobili,  and  improved  by  Melloni, 
consists  essentially  of  a  chain  (Fig. 
284)  formed  of  alternate  elements 
of  bismuth  and  antimony.  If  the 
ends  of  the  chain  be  connected  by 
a  wire,  and  the  alternate  joints 
slightly  heated,  a  thermo-electric 
current  will  be  produced,  as  will  be 
explained  hereafter.  The  amount 
of  current  increases  with  the  num- 
ber of  elements,  and  with  the  difference  of  temperatures  of  the  oppo- 
site junctions. 

In  the  pile  as  improved  by  Melloni,  the  elements  are  arranged 
side  by  side  so  as  to  form  a  square  bundle  (Fig.  285),  whose  opposite 


Fig.  284.— Nobili's  Thermo-electric  Series. 


Fig.  2S5.— Melloni's  Thermo-multiplier. 


ends  consist  of  the  alternate  junctions.  The  whole  is  contained  in 
a  copper  case,  with  covers  at  the  two  ends,  which  can  be  removed 
when  it  is  desired  to  expose  the  faces  of  the  pile  to  the  action  of  heat. 


398 


RADIANT  HEAT. 


Two  metallic  rods  connect  the  terminals  of  the  thermo-electric  series 
with  wires  leading  to  a  galvanometer,1  so  that  the  existence  of  any 
current  will  immediately  be  indicated  by  the  deflection  of  the  needle. 
The  amounts  of  current  which  correspond  to  different  deflections  are 
known  from  a  table  compiled  by  a  method  which  we  shall  explain 
hereafter.  Consequently,  when  a  beam  of  radiant  heat  strikes  the 
pile,  an  electric  current  is  produced,  and  the  amount  of  this  current 
is  given  by  the  galvanometer.  We  shall  see  hereafter,  when  we 
come  to  treat  of  thermo-electric  currents,  that  within  certain  limits, 
which  are  never  exceeded  in  investigations  upon  radiant  heat,  the 
current  is  proportional  to  the  difference  of  temperature  between  the 
two  ends  of  the  pile.  Accordingly,  as  soon  as  all  parts  of  the  pile 
have  acquired  their  permanent  temperatures,  the  quantity  of  heat 
received  during  any  interval  of  time  from  the  source  of  heat  will  be 
equal  to  that  lost  to  the  air  and  surrounding  objects.  But  this  latter 
is,  by  Newton's  law,  proportional  to  the  excess  of  temperature  above 
the  surrounding  air,  and  therefore  to  the  difference  of  temperature 
between  the  two  ends  of  the  pile.  The  current  is  therefore  propor- 
tional to  the  quantity  of  heat  received  by  the  instrument.  We  have 
thus  in  Nobili's  pile  a  thermometer  of  great  delicacy,  and  admirably 
adapted  to  the  study  of  radiant  heat ;  in  fact,  the  immense  progress 


Fig.  286.—  Measurement  of  Emissive  Powers. 

which  has  been  made  in  this  department  of  physics  is  mainly  owing 
to  this  invention  of  Nobili. 

314.  Measurement  of  Emissive  Power. — The  following  arrangement 
was  adopted  by  Melloni  for  the  comparison  of  emissive  powers.     A 

1  The  pile  and  galvanometer  together  constitute  the  thermo- multiplier. 


EMISSIVE   AND   ABSORBING   POWERS.  399 

graduated  horizontal  bar  (Fig.  286)  carries  a  cube,  the  different  sides 
of  which  are  covered  with  different  substances.  This  is  filled  with 
water,  whicli  is  maintained  at  the  boiling-point  by  means  of  a  spirit- 
lamp  placed  beneath.  The  pile  is  placed  at  a  convenient  distance, 
and  the  radiation  can  be  intercepted  at  pleasure  by  screens  arranged 
for  the  purpose.  The  whole  forms  what  is  called  Melloni's  appa- 
ratus. 

If  we  now  subject  the  pile  to  the  heat  radiated  from  each  of  the 
faces  in  turn,  we  shall  obtain  currents  proportional  to  the  emissive 
powers  of  the  substances  with  which  the  different  faces  are  coated. 

From  a  number  of  experiments  of  this  kind  it  has  been  found  that 
lamp-black  has  the  greatest  radiating  power  of  all  known  substances, 
while  the  metals  are  the  worst  radiators.  Some  of  the  most  impor- 
tant results  are  given  in  the  following  table,  in  which  the  emissive 
powers  of  the  several  substances  are  compared  with  that  of  lamp- 
black, which  is  denoted  by  100: — 

KELATIVE  EMISSIVE  POWERS  AT  100°  C. 

Lamp-black, 100  Steel, 17 

White-lead, 100  Platinum, 17 


Paper, 98 

Glass, 90 

Indian  ink, 85 

Shellac, 72 


Polished  brass,       ....  7 

Copper, 7 

Polished  gold, 3 

Polished  silver,      ....  3 


316.  Absorbing  Power. — The  method  which  most  naturally  suggests 
itself  for  comparing  absorbing  powers,  is  to  apply  coatings  of  different 
substances  to  that  face  of  the  pile  which  is  exposed  to  the  action  of 
the  source  of  heat.  But  this  would  involve  great  risk  of  injury  to 
the  pile. 

The  method  employed  by  Melloni  was  as  follows: — He  placed  in 
front  of  the  pile  a  very  thin  copper  disc  (Fig.  287),  coated  with  lamp- 
black on  the  side  next  the  pile,  and  on  the  other  side  with  the  sub- 
stance whose  absorbing  power  was  required.  The  disc  absorbed  heat 
by  radiation  from  the  source,  of  amount  proportional  to  the  absorb- 
ing power  of  this  coating,  and  at  the  same  time  emitted  heat  from 
both  sides  in  all  directions.  When  its  temperature  became  stationary, 
the  amounts  of  heat  absorbed  and  emitted  were  necessarily  equal, 
and  its  two  faces  had  sensibly  equal  temperatures. 

Let  E  and  E'  denote  the  coefficients  of  emission  of  lamp-black  and 
of  the  substance  with  which  the  front  was  coated,  and  0  the  excess 
of  temperature  of  the  disc  a-bove  that  of  the  air;  then  (E-f-E')0  is  the 


400 


RADIANT  HEAT. 


heat  emitted  in  unit  time,  if  the  area  of  each  face  is  unity,  and  this 
must  be  equal  to  the  heat  absorbed  in  unit  time. 

But  the  indications  of  the  thermo-pile  are  proportional  to  the  heat 


Fig.  287. — Measurement  of  Absorbing  Powers. 

radiated  from  the  back  alone,  that  is,  to  E0.     The  heat  absorbed  is 
therefore  represented  by  the  indication  of  the  pile  multiplied  by 

E_+JE' 
E 

In  this  way  the  absorbing  powers  given  in  the  following  list  have 
been  calculated  from  experiments  of  Melloni,  the  source  of  heat  being 
a  cube  filled  with  water  at  100°  C. 

KELATIVE  ABSORBING  POWERS  AT  100°  C. 


Lamp-black,       ....     100 

White-lead, 100 

Isinglass, 91 


Indian  ink, 85 

Shellaq, 72 

Metal, 13 


It  will  be  observed  that  these  numbers  are  identical  with  those  which 
represent  the  emissive  powers  of  the  same  substances. 

317.  Variation  of  Absorption  with  the  Source. — The  absorbing 
power  varies  according  to  the  source  of  heat  employed.  In  estab- 
lishing this  important  fact,  MeUoni  employed  the  following  sources  of 
heat: — 

1.  Locatelli's  lamp,  a  small  kind  of  oil-lamp,  in  which  the  level  of 
the  oil  remains  invariable,  and  which  has  a  square-cut  solid  wick. 
As  a  source  of  heat  it  is  of  tolerably  constant  action,  and  it  has  been 
employed  in  most  of  the  experiments  upon  diathermancy.  It  is 
shown  in  Fie.  287. 


VAEIATION   OF  ABSORPTION. 


401 


2.  Incandescent  platinum.     This  is  a  spiral  of  platinum  wire  (Fig. 
288)  suspended  over  a  spirit-lamp  so  as  to  envelop  the  flame.     The 
metal  is  heated  to  a  bright  white  heat;    and  since  the  radiating 
powers  of  the  flame  are  very  feeble,  the  metal  may  be  regarded  as 
the  sole  source  of  radiation.     The  flame,  in  fact,  is  scarcely  distin- 
guishable. 

O 

3.  Copper  heated  to  about  400°  C.     This  is  effected  by  placing  a 
spirit-lamp  behind  a  curved  copper  plate  (Fig.  289). 

4.  Copper  covered  with  lamp-black  at  100°  C«     This  is  a  cube  con- 
taining boiling  water  (Fig.  290)  similar  to  that  already  described  in 


Fig.  288. 
Incandescent  Platini 


Fig.  289. 
Copper  heated  to  400°. 


Fig.  290. 
Cube  at  100°.. 


connection  with  the  measurement  of  emissive  powers.    The  face  whose 
radiation  is  employed  is  covered  with  lamp-black. 

If  these  different  sources  of  heat  be  severally  used  in  measuring 
absorbing  powers,  it  will  be  found  that  these  powers  vary  consider- 
ably according  to  the  particular  source  of  heat  employed,  and  that  if 
we  denote  the  absorption  of  lamp-black  in  each  case  by  100,  the 
relative  absorbing  powers  of  other  substances  are  in  general  greater 
as  the  temperature  of  the  source  is  lower.  In  establishing  this 
important  principle  by  experiment,  the  sources  of  heat  are  first 
placed  at  such  distances  that  the  direct  radiation  upon  the  pile 
shall  be  the  same  for  each,  and  the  pile  is  then  replaced  by  the 
disc.  The  following  table  contains  some  of  the  results  obtained 

by  Melloni : — 

26 


402 


RADIANT  HEAT. 


SUBSTANCES. 

Locatelli's 
Lamp. 

Incandescent 
Platinum. 

Heated 
Copper. 

Hot-  water 
Cube. 

Lamp-black,  .     . 

100 

100 

100 

100 

Indian  ink, 

96 

95 

87 

85 

White-lead,     .     . 

53 

56 

89 

100 

Isinglass,   .     .     . 

52 

54 

64 

91 

Shellac,      .     .     . 

48 

47 

70 

72 

Metallic  surface, 

14 

13-5 

13 

13 

319.  Reflecting  Power. — The  reflecting  power  of  a  surface  is  mea- 
sured by  the  proportion  of  incident  heat  which  is  regularly  reflected 
from  it.  This  subject  has  been  investigated  by  Melloni,  and  by 
Laprovostaye  and  Desains.  The  arrangement  used  for  the  purpose  is 
shown  in  Fig.  291. 

The  substance  under  investigation  is  placed  upon  the  circular  plate 
D,  which  is  graduated  round  the  circumference.  The  pile  E  is  carried 


Fig.  291.— Measurement  of  Reflecting  Power. 

by  the  horizontal  bar  H  H',  which  turns  about  the  pillar  supporting 
the  plate  D.  This  bar  is  to  be  so  adjusted  as  to  make  the  reflected  rays 
impinge  upon  the  pile,  the  adjustment  being  made  by  the  help  of 
the  divisions  marked  on  the  circular  plate. 

Tn  making  an  observation,  the  bar  HH'  is  first  placed  so  as  to 
coincide  witli  the  prolongation  of  the  principal  bar,  and  the  intensity 
of  direct  radiation  is  thus  observed.  The  pile  is  then  placed  so  as  to 
receive  the  reflected  rays,  and  the  ratio  of  the  intensity  thus  obtained 
to  the  intensity  of  direct  radiation  is  the  measure  of  the  reflecting 
power. 


REFLECTING   POWER. 


403 


The  following  are  some  of  the  results  obtained  by  Laprovostaye 
and  Desains,  the  source  of  heat  employed  being  a  Locatelli  lamp: — 


Polished  platinum,  . 

Steel, 

Zinc, 

Iron, 


Reflecting 
Power. 

.  -80 
.  -83 
.  -81 

•77 


Reflecting 
Power. 

Silver  plate, "97 

Gold, -95 

Brass, -93 

Speculum  metal,      .     .     .  "86 

Tin, -85 

Laprovostaye  and  Desains  have  also  shown  that,  in  the  case  of 
diathermanous  substances,  the  reflecting  power  varies  considerably 
with  the  angle  of  incidence,  which  is  also  the  case  for  luminous  rays. 

In  the  case  of  metals,  the  change  in  the  reflecting  powrer  produced 
by  a  change  in  the  angle  of  incidence  is  not  nearly  so  great;  the 
reflecting  power  remains  almost  constant  till  about  70°  or  80°,  and 
when  the  angle  of  incidence  exceeds  this  limit,  the  reflecting  power 
decreases,  whereas  the  opposite  is  the  case  with  transparent  bodies. 

Finally,  Laprovostaye  and  Desains  have  shown  that,  contrary  to 
what  was  previously  supposed,  the  reflecting  power  varies  according 
to  the  source  of  heat.  Thus  the  reflecting  power  of  polished  silver, 
which  is  '97  for  rays  from  a  Locatelli  lamp,  is  only  *92  for  solar  rays. 
In  either  case  it  will  be  seen  that  the  reflecting  powers  of  polished 
silver  are  very  great ;  and  since  experiment  has  shown  that  luminous 
and  calorific  rays  from  the  same  source  are  reflected  in  nearly  equal 
proportions,  the  advantages  attending  the  use  of  silvered  specula  in 
telescopes  can  easily  be  understood. 

320.  Diffusive  Power. — Diffusion  is  the  irregular  reflection  of  heat, 
doubtless  owing  to  the  minute  inequalities  of  surface  which  are  met 
with  on  even  the  most  finely-polished  bodies.  The  existence  of  this 
power  may  very  easily  be  verified.  We  have  only  to  let  a  beam  of 
radiant  heat  fall  upon  any  dead  surface,  for  example  on  carbonate  of 
lead.  On  placing  the  pile  before  the  surface  in  any  position,  a  devia- 
tion of  the  galvanometer  is  observed,  which  cannot  be  attributed  to 
radiation  from  the  surface,  since  in  that  case  the  effect,  instead  of 
instantly  attaining  its  maximum,  as  it  actually  does,  would  increase 
gradually  as  the  substance  became  warmed  by  the  heat  falling  upon  it. 

Moreover  the  heat  thus  diffused,  when  the  source  of  heat  is  a  body 
at  high  temperature,  such  as  a  lamp-flame,  is  found  to  agree  in  'its 
properties  with  the  heat  radiated  from  a  body  at  high  temperature, 
and  to  be  altogether  different  from  that  which  the  diffusing  surface 
is  capable  of  radiating  at  its  actual  temperature.  The  diffused  heat, 


404  RADIANT    HEAT. 

for  example,  passes  through  a  plate  of  alum  without  undergoing  much 
absorption. 

The  diffusive  power  of  powders,  especially  if  white,  is  very  con- 
siderable, as  is  shown  by  the  following  table  taken  from  the  results 
published  by  Laprovostaye  and  Desains: — 

DIFFUSIVE  POWER. 

White-lead,      . '82 

Powdered  silver,       .          .         .         .         .         .  "76 

Chromate  of  lead,     .         .         .         .         .         .  '66 

The  knowledge  of  this  property  enables  us  to  explain  the  intense 
heat  which  is  felt  in  the  neighbourhood  of  a  white  wall  lighted  up 
by  the  sun. 

Diffusion  takes  place  in  different  proportions  according  to  the 
direction,  and  is  a  maximum  for  points  near  the  direction  of  the 
regularly-reflected  ray. 

The  intensity  of  the  diffused  rays  varies  very  considerably  accord- 
ing to  the  source  of  heat  employed.  This  was  shown  by  Melloni  in 
the  following  manner: — 

He  directed  a  ray  of  heat  upon  the  surface  of  a  disc  of  very  thin 
card  covered  with  a  substance  capable  of  diffusing  the  rays.  The 
back  of  the  disc  was  coated  with  lamp-black.  When  the  different 
parts  had  acquired  their  permanent  temperatures,  the  pile  was  placed 
in  corresponding  positions  first  before,  and  then  behind  the  disc,  so 
as  to  receive  the  heat  due  to  both  radiation  and  diffusion  from  the 
disc  in  the  first  case,  and  that  due  to  radiation  only  in  the  second. 
It  was  found  that  the  ratio  of  the  two  indications  of  the  pile  in  these 
two  positions  varied  very  much  according  to  the  source  of  heat,  the 
general  rule  being  that  the  ratio  of  the  diffused  to  the  radiated  heat 
was  greatest  when  the  source  of  heat  was  luminous,  and  at  a  high 
temperature. 

321.  Peculiar  Property  of  Lamp-black. — If  a  similar  experiment  be 
performed  with  a  card  covered  on  both  sides  with  lamp-black,  it  will 
be  found  that  the  difference  between  the  indications  of  the  pile  in 
the  two  positions  is  very  small.  This  difference,  such  as  it  is,  may 
be  accounted  for  by  a  slight  difference  of  temperature  between  the 
two  faces  of  the  disc.  We  may  therefore  conclude  that  the  whole  of 
the  heat  has  been  absorbed  by  the  lamp-black.  This  important  result 
has  been  confirmed  by  direct  experiments,  which  have  failed  to  dis- 
cover any  trace  of  reflecting  or  diffusive  power  in  this  substance. 
Further,  in  the  above  experiment,  the  ratio  of  the  indications  in  the 


DIATHERMANCY. 


405 


two  positions  of  the  pile  remains  constant  for  all  sources  of  heat; 
whence  we  see  that  the  absorption  of  rays  of  heat  by  lamp-black  is 
in  all  cases  independent  of  the  nature  of  the  source.  We  thus  see 
the  advantage  of  applying  a  coating  of  lamp-black  to  all  thermoscopic 
apparatus  intended  for  the  absorption  of  radiant  heat. 

322.  Diathermancy. — It  has  long  been  known  that  some  of  the  heat 
from  an  intensely  luminous  body,  like  the  sun,  could  pass  through 
certain  transparent  substances,  such  as  glass ;  but  it  was,  till  recently, 
supposed  that  this,  could  not  happen  in  the  case  of  dark,  or  even 
feebly  luminous  rays. 

Pictet,  of  Geneva,  was  the  first  to  establish  the  fact  of  diathermancy 
for  radiant  heat  in  general.  He  showed  that  a  thermometer  rose  in 
temperature  when  exposed  to  radiation  from  a  source  of  heat,  not- 
withstanding the  interposition  of  a  transparent  lamina;  and  the  idea 
that  this  could  be  owing  to  the  absorption  and  subsequent  radiation 
of  heat  from  the  lamina  was  completely  exploded  by  Prevost,  who 
showed  that  the  effect  occurred  even  when  the  interposed  substance 
was  a  sheet  of  ice.  It  is  to  Melloni,  however,  that  we  are  indebted 
for  the  principal  results  which  have  been  obtained  in  connection  with 
this  subject. 

323.  Influence  of  the  Nature  of  the  Substance. — The  arrangement 
adopted  by  Melloni  for  testing  the  diathermancy  of  a  solid  body  is 
that  shown  in  Fig.  292.     The  Locatelli  lamp  A  radiates  its  heat  upon 


Fig.  292. — Measurement  of  Diathermancy. 


the  pile  E  when  the  screen  B  is  lowered;  the  hole  in  the  screen  C  is 
for  the  purpose  of  limiting  the  pencil  of  rays.  Direct  radiation  is 
first  allowed  to  take  place,  and  the  resulting  current  as  indicated  by 


406 


RADIANT  HEAT. 


the  galvanometer  G  is  noted.  The  diathermanous  plate  D  is  then 
interposed  between  the  lamp  and  the  pile,  and  the  current  is  again 
measured ;  the  ratio  of  the  latter  current  to  the  former  is  the  expres- 
sion of  the  diathermancy  of  the  plate. 

In  the  case  of  liquids,  Melloni  employed  narrow  troughs  with  sides 
of  very  thin  glass;  the  rays  were  first  transmitted  through  the  empty 
vessel,  and  then  through  the  same  vessel  filled  with  liquid ;  the  dif- 
ference of  the  two  results  thus  obtained  being  the  measure  of  the  heat 
stopped  by  the  liquid.  Specimens  of  the  results  are  given  in  the 
following  table :  — 

HEAT  TRANSMITTED  BY  DIFFERENT  SUBSTANCES  FROM  AN  ARGAND  LAMP. 
(The  direct  heat  is  represented  by  100.) 


SOLIDS. 

Colourless  Glass. 
(Thickness  1-83  mm.) 

Flint-glass, from  67  to  64 

Plate-glass, 62  to  59 

Crown-glass  (French), 58 

Crown  glass  (English), 49 

Window- glass, 54  to  50 

Coloured  Glass. 
(Thickness  TS5  mm.) 

Deep  violet, 53 

Pale  violet, 45 

Very  deep  blue, 19 

Deep  blue, 33 

Light  blue, 42 

Mineral  green, 23 

Apple  green, 26 

Deep  yellow, 40 

Orange, 44 

Yellowish  red, «...  53 

Crimson, .     ,      ,51 


LIQUIDS. 
(Thickness  9  21  mm. — A  plate  of  glass  of  the  same 

thickness  gives  53.) 
Colourless  Liquids 

Distilled  water, 11 

Absolute  alcohol, 15 

Sulphuric  ether, 21 

Sulphide  of  carbon, 63 

Spirits  of  turpentine, 31 

Pure  sulphuric  acid, 17 

Pure  nitric  acid, 15 

Solution  of  sea-salt, 12 

Solution  of  alum, 12 

Solution  of  sugar, 12 

Solution  of  potash, 13 

Solution  of  ammonia, 15 

Coloured  Liquids. 

Nut-oil  (yellow) 31 

Colza-oil  (yellow) 30 

Olive-oil  (greenish  yellow), 
Oil  of  carnations  (yellowish)  . 
Chloride  of  sulphur  (reddish  brown), 
Pyroligneous  acid  (brown),     .     .     . 
White  of  egg  (slightly  yellow),   .     . 


CRYSTALLIZED  BODIES. 

(Thickness  3'62  mm.— A  plate  of  glass  of  the  same  thickness  gives  62.) 


Colourless. 

Rock-salt,       .     .     .     , 92 

Iceland- spar,        12 

Rock-crystal, 57 

Brazilian  topaz,        54 

Carbonate  of  lead, 52 

Borate  of  soda, 28 

Sulphate  of  lime, 20 

Citric  acid, 15 

Hock  alum, 12 


Coloured. 

Smoky  quartz  (brown), 57 

Aqua-marina  (light  blue),       ....  29 

Yellow  agate, 29 

Green  tourmaline, 27 

Sulphate  of  copper  (blue) 0 


DIATHERMANCY.  407 

It  will  be  seen  from  this  table  that  though  diathermancy  and 
transparency  for  light  usually  go  together,  the  one  is  far  from  being 
a  measure  of  the  other.  We  see,  for  instance,  that  colourless  nitric 
acid  is  much  less  diathermanous  than  strongly-coloured  chloride  of 
sulphur;  and  perfectly  colourless  alum  allows  much  less  heat  to  pass 
than  deeply-coloured  glass  of  the  same  thickness.  Tyndall  has  shown 
that  a  solution  of  iodine  in  sulphide  of  carbon,  though  excessively 
opaque  to  light,  allows  heat  to  pass  in  large  quantity. 

The  substance  possessing  the  greatest  diathermanous  power  is  rock- 
salt,  which  allows  the  passage  of  *92  of  the  incident  heat.  Common 
sea-salt  only  allows  -1 2  to  pass.  No  such  difference,  however,  at- 
taches to  solutions  of  these  substances. 

The  diathermancy  of  gases  has  been  investigated  by  Tyndall.  The 
gases  were  contained  in  a  long  metallic  tube  with  rock-salt  ends; 
and,  in  order  to  obtain  greater  sensitiveness,  a  compensating  cube 
filled  with  hot  water  was  employed.  This  cube  was  placed  at  such 
a  distance  from  one  end  of  the  thermo-pile  as  exactly  to  counter- 
balance the  effect  of  the  radiation  from  the  principal  source  of  heat 
when  the  tube  was  vacuous,  so  that  the  needle  of  the  galvanometer 
in  these  circumstances  stood  at  zero.  The  tube  was  then  filled  with 
different  gases  in  turn,  the  compensating  cube  remaining  unmoved ; 
and  the  indications  of  the  galvanometer  were  found  to  vary  accord- 
ing to  the  gas  employed.  Compound  gases  stopped  more  than  simple 
ones;  the  vapours  of  aromatic  substances  increased  the  absorptive 
power  of  dry  air  from  30  to  300  fold,  and  a  similar  effect  was  pro- 
duced by  the  vapour  of  water,  air  more  or  less  charged  with  aqueous 
vapour  being  found  to  exercise  from  30  to  70  times  the  absorption 
of  pure  dry  air. 

It  is  probable  that  the  aqueous  vapour  which  is  always  present  in 
the  atmosphere  greatly  mitigates  the  heat  of  the  solar  rays,  and  also 
greatly  retards  the  cooling  of  the  earth  by  radiation  at  night.  On 
the  other  hand,  vapour  being  a  better  absorber  is  also  a  better 
radiator  than  dry  air,  a  circumstance  which  conduces  to  the  cooling 
and  condensation  of  the  upper  portions  of  masses  of  vapour  in  the 
atmosphere,  and  the  consequent  formation  of  cloud. 

324.  Influence  of  Thickness. — From  the  experiments  of  Jamin  and 
Masson,  it  appears  that,  when  heat  of  definite  refrangibility  passes 
through  a  plate,  the  amount  transmitted  decreases  in  geometrical 
progression  as  the  thickness  increases  in  arithmetical  progression;  a 
result  which  may  also  be  expressed  by  saying,  that  if  a  plate  be 


408  RADIANT   HEAT. 

divided  in  imagination  into  laminae  of  equal  thickness,  the  ratio  of 
the  heat  absorbed  to  the  heat  transmitted  is  the  same  for  them  all. 

In  the  case  of  mixed  radiation,  such  as  is  emitted  by  nearly  all 
available  sources  of  heat,  we  must  suppose  this  law  to  hold  for  each 
separate  constituent ;  but  some  of  these  are  more  easily  absorbed  than 
others,  and  as  these  accordingly  diminish  in  amount  more  rapidly 
than  the  others,  the  beam  as  it  proceeds  on  its  way  through  the  plate 
acquires  a  character  which  fits  it  for  transmission  rather  than  absorp- 
tion. Hence  the  foremost  layers  absorb  much  more  than  the  later 
ones,  if  the  plate  be  of  considerable  thickness. 

In  the  case  of  bodies  which  are  opaque  to  heat,  absorption  and 
radiation  are  mere  surface-actions.  But  in  diathermanous  substances, 
as  we  have  seen,  absorption  goes  on  in  the  interior,  so  that  a  thick 
plate  absorbs  more  heat  than  a  thin  one.  The  same  thing  is  true  as 
regards  radiation: — a  diathermanous  substance  radiates  from  its 
interior  as  well  as  from  its  surface,  as  proved  by  the  fact  that  a  thick 
plate  radiates  more  heat  than  a  thin  one  at  the  same  temperature. 

325.  Relation  between  Radiant  Heat  and  Light. — The  property  in 
virtue  of  which  particular  substances  select  particular  kinds  of  heat 
for  absorption  and  other  kinds  for  transmission,  was  called  by  Melloni 
thermochrose  (literally  heat-colour),  from  its  obvious  analogy  to  what 
we  call  colour  in  the  case  of  light.  A  piece  of  coloured  glass,  for 
example,  selects  rays  of  certain  colours  (or  vibration-periods)  for 
absorption,  and  transmits  the  rest,  what  we  call  the  colour  of  the 
glass  being  determined  by  those  which  it  transmits. 

It  is  now  believed  that  thermochrose  and  colour  are  not  merely 
analogous  but  essentially  identical.  Prismatic  analysis  shows  that 
rays  exist  of  refrangibilities  much  greater  and  much  less  than  those 
which  compose  the  luminous  spectrum.  The  spectrum  of  the  electric 
light,  for  example,  extends  on  both  sides  of  the  visible  spectrum  to 
distances  considerably  exceeding  the  length  of  the  visible  spectrum 
itself.  The  invisible  ultra-violet  rays  can  be  detected  by  their 
chemical  action,  or  by  causing  them  to  fall  upon  certain  substances 
(called  fluorescent)  which  become  luminous  when  exposed  to  their 
action,  but  have  exceedingly  small  heating  effect.  The  heat  becomes 
considerable  in  the  yellow  portion  of  the  spectrum,  stronger  in  the 
red,  and  goes  on  increasing  in  the  invisible  portion  beyond  the  red, 
up  to  a  certain  point,  beyond  which  it  gradually  diminishes  till  it 
becomes  inappreciable. 

It  would,  however,  be  an  error  to  suppose  that  there  is  a  heat 


RADIANT   HEAT  AND   LIGHT.  409 

spectrum  consisting  of  distinct  rays  from  those  which  form  the  lumin- 
ous spectrum,  and  that  the  two  spectra  are  superimposed  one  upon 
the  other.  There  is  every  reason  for  believing  that  the  contrary  is 
the  fact,  and  that  the  radiations  which  constitute  heat  and  light  are 
essentially  identical.  In  operating  upon  rays  of  definite  refrangibi- 
lity,  it  is  never  found  possible  to  diminish  their  heating  and  illumi- 
nating powers  in  unequal  proportions;  an  interposed  plate  of  any 
partially  transparent  material,  if  it  stops  half  the  light,  also  stops 
half  the  heat. 

It  is  true  that  the  most  intense  heat  is  not  found  in  the  most 
luminous  portion  of  the  spectrum ;  but  it  is  probable  that  the  eye, 
like  the  ear,  is  more  powerfully  affected  by  quick  than  by  slow 
vibrations  when  the  amount  of  energy  is  the  same ;  and  as  a  treble 
note  contains  far  less  energy  than  a  bass  note  which  strikes  the  ear 
as  equally  loud,  so  a  blue  ra}7  contains  much  less  energy  than  a  red 
ray  if  they  strike  the  eye  as  equally  bright. 

The  invisibility — at  least  to  human  eyes — of  the  ultra-red  and 
ultra-violet  rays  may  be  due  either  to  the  absorption  of  these  rays 
by  the  humours  of  the  eye  before  they  can  reach  the  retina,  or  to  the 
inability  of  our  visual  organs  to  take  up  vibrations  quicker  than  the 
violet  or  slower  than  the  red. 

A  body  at  a  low  temperature  (say  100°  C.)  emits  only  dark  heat. 
As  the  temperature  rises,  the  emission  of  dark  heat  becomes  more 
energetic,  and  at  the  same  time  rays  of  a  more  refrangible  character 
are  added.  This  strengthening  of  the  rays  formerly  emitted,  with 
the  continual  addition  of  new  rays  of  higher  refrangibility,  goes  on 
as  long  as  the  temperature  of  the  body  continues  to  rise.  The  lumi- 
nosity of  the  body  begins  with  the  emission  of  the  least  refrangible 
of  the  visible  rays,  namely  the  red,  and  goes  on  to  include  rays  of 
other  colours  as  it  passes  from  a  red  to  a  white  heat.  Tyndall,  by 
thus  gradually  raising  the  temperature  of  a  platinum  spiral,  obtained 
the  following  measures  of  the  heat  received  in  a  definite  position  in 
the  dark  portion  of  the  spectrum : — 


Appearance  Heat 

of  Spiral.  Received. 

Dark, 1 

Dark, 6 

Faint  red, 10 

Dull  red, 13 


Appearance  Heat 

of  Spiral.  Received. 

Full  red, 27 

Orange, 60 

Yellow, 93 

Full  white, 122 


Red, 18 

Generally  speaking,  the  rays  which  fall  within  the  limits  of  the 


410  RADIANT   HEAT. 

visible  spectrum  are  the  most  transmissible,  and  the  extreme  rays  at 
both  ends  of  the  complete  spectrum  are  the  soonest  absorbed.  This 
is  probably  the  reason  why  the  invisible  portion  of  the  solar  spec- 
trum, though  extending  to  a  considerable  distance  in  both  directions, 
is  less  extensive  than  that  of  the  electric  light.  The  extreme  rays 
have  probably  been  absorbed  by  the  earth's  atmosphere. 

Ordinary  glass  is  comparatively  opaque  to  both  classes  of  dark 
rays.  Bock-salt  surpasses  all  other  substances  in  its  transparency 
to  the  dark  rays  beyond  the  red;  and  quartz  (rock-crystal)  is  very 
transparent  to  the  dark  rays  beyond  the  violet.  Alum  is  remarkable 
as  a  substance  which  is  exceedingly  opaque  to  the  ultra-red  rays, 
though  exceedingly  transparent  to  visible  rays;  and  Tyndall  has 
found  that  a  solution  of  iodine  in  sulphide  of  carbon  is,  on  the  con- 
trary, highly  transparent  to  the  ultra-red  and  opaque  to  the  luminous 
rays. 

Great  interest  was  excited  some  years  ago  by  Stokes'  discovery 
that  the  ultra-violet  rays,  when  they  fall  upon  fluorescent  substances, 
undergo  a  lowering  of  refrangibility  which  brings  them  within  the 
limits  of  human  vision.  Akin  subsequently  proposed  the  inquiry 
whether  it  was  possible,  by  a  converse  change,  to  transform  the 
ultra-red  into  visible  rays,  and  Tyndall,  by  taking  advantage  of  this 
peculiar  property  of  the  solution  of  iodine,  succeeded  in  effecting  the 
transformation.  He  brought  the  rays  of  the  electric  lamp  to  a  focus 
by  means  of  a  reflector,  and,  after  stopping  all  the  luminous  rays  by 
interposing  a  vessel  with  rock-salt  sides,  containing  the  solution  of 
iodine,  he  found  that  a  piece  of  platinum  foil,  when  brought  into  the 
focus,  was  heated  to  incandescence,  and  thus  emitted  light  as  well  as 
heat.  To  this  transformation  of  dark  radiant  heat  into  light  he  gave 
the  name  of  calorescence. 

326.  Selective  Emission  and  Absorption. — In  order  to  connect 
together  the  various  phenomena  which  may  be  classed  under  the 
general  title  of  selective  radiation  and  absorption,  it  is  necessary  to 
form  some  such  hypothesis  as  the  following.  The  atoms  or  mole- 
cules of  which  any  particular  substance  is  composed,  must  be  sup- 
posed to  be  capable  of  vibrating  freely  in  certain  periods,  which,  in 
the  case  of  gases,  are  sharply  defined,  so  that  a  gas  is  like  a  musical 
string,  which  will  vibrate  in  unison  with  certain  definite  notes  and 
with  no  intermediate  ones.  The  particles  of  a  solid  or  liquid,  on  the 
other  hand,  are  capable  of  executing  vibrations  of  any  period  lying 
between  certain  limits;  so  that  they  may  perhaps  be  compared  to  the 


SELECTIVE  EMISSION   AND  ABSORPTION.  411 

body  of  a  violin,  or  to  the  sounding-board  of  a  piano ;  and  these  limits 
(or  at  all  events  the  upper  limit)  alter  with  the  temperature,  so  as 
to  include  shorter  periods  of  vibration  as  the  temperature  rises. 

These  vibrations  of  the  particles  of  a  body  are  capable  of  being 
excited  by  vibrations  of  like  period  in  the  external  ether,  in  which 
case  the  body  absorbs  radiant  heat.  But  they  may  also  be  excited 
by  the  internal  heat  of  the  body ;  for  whenever  the  molecules  expe- 
rience violent  shocks,  which  excite  tremors  in  them,  these  are  the 
vibrations  which  they  tend  to  assume.  In  this  case  the  particles  of 
the  body  excite  vibrations  of  like  period  in  the  surrounding  ether, 
and  the  body  is  said  to  emit  radiant  heat. 

One  consequence  of  these  principles  is  that  a  diathermanous  body 
is  particularly  opaque  to  its  own  radiation.  Rock-salt  transmits  92 
per  cent,  of  the  radiation  from  most  sources  of  heat;  but  if  the  source 
of  heat  be  another  piece  of  rock-salt,  especially  if  it  be  a  thin  plate, 
the  amount  transmitted  is  much  less,  a  considerable  proportion  being 
absorbed.  The  heat  emitted  and  absorbed  by  rock-salt  is  of  exceed- 
ingly low  refrangibility. 

Glass  largely  absorbs  heat  of  long  period,  such  as  is  emitted  by 
bodies  whose  temperatures  are  not  sufficiently  high  to  render  them 
luminous,  but  allows  rays  of  shorter  period,  such  as  compose  the 
luminous  portion  of  the  radiation  from  a  lamp-flame,  to  pass  almost 
entire.  Accordingly  glass  when  heated  emits  a  copious  radiation  of 
non-luminous  heat,  but  comparatively  little  light. 

Experiment  shows  that  if  various  bodies,  whether  opaque  or  trans- 
parent, colourless  or  coloured,  are  heated  to  incandescence  in  the 
interior  of  a  furnace,  or  of  an  ordinary  coal-fire,  they  will  all,  while 
in  the  furnace,  exhibit  the  same  tint,  namely  the  tint  of  the  glowing 
coals.  In  the  case  of  coloured  transparent  bodies,  this  implies  that 
the  rays  which  their  colour  prevents  them  from  transmitting  from 
the  coals  behind  them  are  radiated  by  the  bodies  themselves  most 
copiously;  for  example,  a  glass  coloured  red  by  oxide  of  copper  per- 
mits only  red  rays  to  pass  through  it,  absorbing  all  the  rest,  but  it 
does  not  show  its  colour  in  the  furnace,  because  its  own  heat  causes 
it  to  radiate  just  those  rays  which  it  has  the  power  of  absorbing,  so 
that  the  total  radiation  which  it  sends  to  the  eye  of  a  spectator,  con- 
sisting partly  of  the  radiation  due  to  its  own  heat,  and  partly  of  rays 
which  it  transmits  from  the  glowing  fuel  behind  it,  is  exactly  the 
same  in  kind  and  amount  as  that  which  comes  direct  from  the  other 
parts  of  the  fire.  This  explanation  is  verified  by  the  fact  that  such 


4)12  RADIANT  HEAT. 

glass,  if  heated  to  a  high  temperature  in  a  dark  room,  glows  with  a 
green  light. 

A  plate  of  tourmaline  cut  parallel  to  the  axis  has  the  property  of 
breaking  up  the  rays  of  heat  and  light  which  fall  upon  it  into  two 
equal  parts,  which  exhibit  opposite  properties  as  regards  polarization. 
One  of  these  portions  is  very  largely  absorbed,  while  the  other  is 
transmitted  almost  entire.  When  such  a  plate  is  heated  to  incan- 
descence, it  is  found  to  radiate  just  that  description  of  heat  and  light 
which  it  previously  absorbed ;  and  if  it  is  heated  in  a  furnace,  no 
traces  of  polarization  can  be  detected  in  the  light  which  comes  from 
it,  because  the  transmitted  and  emitted  light  exactly  complement 
each  other,  and  thus  compose  ordinary  or  unpolarized  light. 

Spectrum  analysis  as  applied  to  gases  furnishes  perhaps  still  more 
striking  illustrations  of  the  equality  of  selective  radiation  and  absorp- 
tion. The  radiation  from  a  flame  coloured  by  vapour  of  sodium — for 
example,  the  flame  of  a  spirit-lamp  with  common  salt  sprinkled  on 
the  wick — consists  mainly  of  vibrations  of  a  definite  period,  corre- 
sponding to  a  particular  shade  of  yellow.  When  vapour  of  sodium  is 
interposed  between  the  eye  and  a  bright  light  yielding  a  continuous 
spectrum,  it  stops  that  portion  of  the  light  which  corresponds  to  this 
particular  period,  and  thus  produces  a  dark  line  in  the  yellow  portion 
of  the  spectrum. 

An  immense  number  of  dark  lines  exist  in  the  spectrum  of  the 
sun's  light,  and  no  doubt  is  now  entertained  that  they  indicate  the 
presence,  in  the  outer  and  less  luminous  portion  of  the  sun's  atmo- 
sphere, of  gaseous  substances  which  vibrate  in  periods  corresponding 
to  the  positions  of  these  lines  in  the  spectrum. 

327.  Dew. — By  this  name  we  denote  those  drops  of  water  which 
are  seen  in  the  morning  on  the  leaves  of  plants,  and  are  especially 
noticeable  in  spring  and  autumn.  We  have  already  seen  (§  298)  that 
dew  does  not  fall,  as  it  is  not  formed  in  the  atmosphere,  but  in  con- 
tact with  the  bodies  on  which  it  appears,  being  in  fact  due  to  their 
cooling  after  the  sun  has  sunk  below  the  horizon,  when  they  lose 
heat  by  radiation  to  the  sky.  The  lowering  of  temperature  which 
thus  occurs,  is  much  more  marked  for  grass,  stones,  or  bare  earth  than 
for  the  air,  whose  radiating  power  is  considerably  less.  The  con- 
sequence is  a  considerable  difference  of  temperature  between  the 
surface  of  the  ground  and  the  air  at  the  height  of  a  few  feet,  a  dif- 
ference which  is  found  by  observation  to  amount  sometimes  to  8°  or 
10°  G,  and  it  is  this  which  causes  the  deposition  of  dew.  The  surface 


DEW.  413 

of  the  earth,  as  it  gradually  cools,  lowers  the  temperature  of  the 
adjacent  air,  which  thus  becomes  saturated,  and,  on  further  cooling, 
yields  up  a  portion  of  its  vapour  in  the  liquid  form.  If  the  tempera- 
ture of  the  soil  falls  below  0°  G,  the  dew  is  frozen,  and  takes  the 
form  of  hoar-frost. 

According  to  this  theory,  it  would  appear  that  the  quantity  of  dew 
deposited  upon  a  body  should  increase  with  the  radiating  power  of 
its  surface,  and  with  its  insulation  from  the  earth  or  other  bodies 
from  which  it  might  receive  heat  by  conduction,  both  which  con- 
clusions are  verified  by  observation. 

The  amount  of  deposition  depends  also  in  a  great  measure  on  the 
degree  of  exposure  to  the  sky.  If  the  body  is  partially  screened,  its 
radiation  and  consequent  cooling  are  checked.  This  explains  the 
practice  which  is  common  with  gardeners  of  employing  light  cover- 
ings to  protect  plants  from  frost — coverings  which  would  be  utterly 
powerless  as  a  protection  against  the  cold  of  the  surrounding  air. 
The  lightness  of  the  dew  on  cloudy  nights  is  owing  to  a  similar  cause ; 
clouds,  especially  when  overhead,  acting  as  screens. 

The  deposition  of  dew  is  favoured  by  a  slight  motion  of  the  atmo- 
sphere, which  causes  the  lower  strata  of  air  to  cool  down  more 
rapidly ;  but  if  the  wind  is  very  high,  the  different  strata  are  so 
intermingled  that  very  little  of  the  air  is  cooled  down  to  its  dew- 
point,  and  the  deposit  is  accordingly  light.  When  these  two  obstacles 
are  combined,  namely  a  high  wind  and  a  cloudy  sky,  there  is  no  dew 
at  all 


CHAPTER    XXX. 


CONDUCTION  OF  HEAT. 


328.  Conduction. — When  heat  is  applied  to  one  end  of  a  bar  of 
metal,  it  is  propagated  through  the  substance  of  the  bar,  producing 
a  rise  of  temperature,  which  is  first  perceptible  at  near  and  afterwards 
at  remote  portions.  This  transmission  of  heat  is  called  conduction, 


and  it  differs  notably  from  radiation  (1),  in  being  gradual  instead  of 
instantaneous;  and  (2),  in  exhibiting  no  preference  for  rectilinear 
transmission,  the  propagation  of  heat  being  as  rapid  through  a 
crooked  as  through  a  straight  bar. 

328  A.  Definition  of  Conductivity  or  Specific  Conducting  Power. — If 
the  application  of  heat  to  one  end  of  the  bar  be  continued  for  a  suffi- 
ciently long  time,  and  with  great  steadiness,  the  different  portions  of 
the  bar  will  at  length  cease  to  rise  in  temperature,  and  will  retain 
steadily  the  temperatures  which  they  have  acquired.  We  may  thus 
distinguish  two  stages  in  the -experiment :  1st,  the  variable  stage, 
during  which  all  portions  of  the  bar  are  rising  in  temperature ;  and, 
2d,  the  permanent  state,  which  may  subsist  for  any  length  of  time 
without  alteration.  In  the  former  stage  the  bar  is  gaining  heat; 
that  is,  it  is  receiving  more  heat  from  the  source  than  it  gives  out 
to  surrounding  bodies.  In  the  latter  stage  the  receipts  and  expendi- 
ture of  heat  are  equal,  and  are  equal  not  only  for  the  bar  as  a  whole, 
but  for  every  small  portion  of  which  it  is  composed. 

In  the  permanent  state  no  further  accumulation  of  heat  takes 
place.  All  the  heat  which  reaches  an  internal  particle  is  transmitted 
by  conduction,  and  the  heat  which  reaches  a  superficial  particle  is 
given  off  partly  by  radiation  and  air-contact,  and  partly  by  conduc- 
tion to  colder  neighbouring  particles.  In  the  earlier  stage,  on  the 
contrary,  only  a  portion  of  the  heat  received  by  a  particle  is  thus 
disposed  of,  the  remainder  being  accumulated  in  the  particle,  and 
serving  to  raise  its  temperature. 


MEASUREMENT   OF   CONDUCTIVITY.  415 

In  order  to  obtain  results  depending  on  conduction  free  from  com- 
plications arising  from  differences  of  specific  heat  (§  340),  we  must, 
in  all  cases,  wait  for  the  permanent  state.  In  the  earlier  stage  great 
specific  heat  acts  as  an  obstacle  to  rapid  transmission,  and  a  body  of 
great  specific  heat  would  be  liable  to  be  mistaken  for  a  body  of  small 
conductivity. 

The  measurement  of  the  conductivity  of  a  substance  is  still  further 
simplified  by  making  the  flow  of  heat  through  it  take  place  entirely 
in  one  definite  direction  (that  is  to  say  in  parallel  lines),  avoiding  all 
cross-currents.  To  this  end  it  is  necessary  that  all  points  in  the  same 
cross  section  should  have  the  same  temperature,  a  condition  which  is 
not  strictly  fulfilled  in  the  bar  above  described,  as  the  surface  will 
be  cooler  than  the  interior.  It  is  nearly  fulfilled  in  the  axial  portions 
of  the  bar,  and  it  is  very  nearly  fulfilled  in  the  central  portions  of  a 
uniform  plate  whose  breadth  in  all  directions  is  a  very  large  multiple 
of  its  thickness,  when  the  whole  of  one  face  is  maintained  as  nearly 
as  practicable  at  one  uniform  temperature,  and  the  other  face  at 
another  uniform  temperature.  In  the  central  portions  of  such  a 
plate,  the  flow  of  heat  will  be  perpendicularly  through  the  plate;  and 
when  the  permanent  state  has  arrived,  the  amount  of  heat  that  passes 
in  a  unit  of  time  through  a  cross  section  of  area  A,  will  be  expressed 
by  the  formula 

Q  =  JfcA^i,  (1) 

where  x  is  the  thickness  of  the  plate,  tl  and  1 2  the  temperatures  of  its 
two  faces,  and  k  a  coefficient  depending  on  the  material  of  the  plate. 
This  coefficient  k  is  the  conductivity  of  the  material.  It  may  be 
defined  as  the  quantity  of  heat  which  flows  in  unit  time  through  a 
cross  section  of  unit  area,  when  the  thickness  of  the  plate  is  unity, 
and  one  face  is  warmer  by  1°  than  the  other.1 

1  The  method  of  taking  account  of  conductivity  during  the  variable  stage  may  be  illus- 
trated by  considering  the  simplest  case, — that  in  which  the  flow  of  heat  is  in  parallel  lines. 

Let  x  denote  distance  measured  in  the  direction  in  which  heat  is  flowing,  v  the  tem- 
perature at  the  time  t  at  a  point  specified  by  x,  k  the  conductivity,  and  c  the  thermal 
capacity  per  unit  volume  (both  at  the  temperature  v).  Then  the  flow  of  heat  per  unit  time 

past  a  cross  section  of  area  A  is  -  Jc  A  C-^,  and  the  flow  past  an  equal  and  parallel  section 

ax 

further  on  by  the  small  distance  8x  is  greater  by  the  amount 

A*   (-**•)«* 

dx  ^         dx' 

This  latter  expression  therefore  represents  the  loss  of  heat  from  the  intervening  prism  AS  a;, 


416  CONDUCTION   OF   HEAT. 

Forbes'  experiments  have  shown  that  the  conductivity  of  a  sub- 
stance is  not  the  same  at  all  temperatures.  In  view  of  this  fact,  k  in 
the  above  formula  denotes  the  average  conductivity  between  the 
temperatures  tl  and  t2.  The  variation  of  conductivity  with  tempera- 
ture is,  however,  comparatively  small. 

329.  Differences  of  Conductivity. — The  following  experiments  are 
often  adduced  in  illustration  of  the  different  conducting  powers  of 
different  solids. 

Two  bars  of  the  same  size  but  of  different  materials  (Fig,  293)  are 
placed  end  to  end,  and  small  wooden  balls  are  attached  by  wax  to 
their  under-surfaces  at  equal  distances.  The  bars  are  then  heated 
at  their  contiguous  ends,  and,  as  the  heat  extends  along  them,  the 


Fig.  293.— Balls  Melted  off. 

wax  melts,  and  the  balls  successively  drop  off.  If  the  heating  is 
continued  till  the  permanent  state  arrives,  it  may  generally  be  con- 
cluded that  the  bar  which  has  lost  most  balls  is  the  best  conductor, 
especially  if  both  bars  have  been  coated  with  the  same  varnish,  so  as 
to  make  their  radiating  powers  equal. 

The  well  known  experiment  of  Ingenhousz  is  of  the  same  kind. 
The  apparatus  consists  of  a  copper  box  having  a  row  of  holes  in  one 
of  its  faces,  in  which  rods  of  different  materials  can  be  fixed.  The 

and  the  resulting  fall  of  temperature  is  the  quotient  of  the  loss  by  the  thermal  capacity 
cA8x,  which  quotient  is 

1     d    (_j.dr\ 

c!Tx\      '  dxj' 

This,  then,  is  the  fall  of  temperature  per  unit  time,  or  is  -  -  v.     If  the  range  of  tem- 

d  t 

perature  is  small  enough  to  admit  of  our  regarding  &  and  c  as  constant,  the  equation 
becomes 

dvjc  d-v 

dt     c  dx*' 

which  applies  approximately  to  the  variations  of  temperature  in  the  soil  near  the  surface  of 
the  earth,  x  being  in  this  case  measured  vertically.  For  the  integral  of  this  equation,  see 
Trans.  Roy.  Soc.  Edin.  vol.  xxii.  part  ii.  p.  438. 


CONDUCTING   POWER   OF   METALS. 


417 


Fig.  294. — Ingenhousz's  Apparatus. 


rods  having  previously  been  coated  with  wax,  the  box  is  filled  with 

boiling  water,  which  comes  into  contact  with  the  inner  ends  of  the 

rods.     The  wax  gradually  _ 

melts  as  the  heat  travels 

along  the  rods ;  and,  if  the 

experiment    is   continued 

till  the  melting  reaches  its 

limit,  those  rods  on  which 

it   has  extended   furth est      IllWPIiPil 

are,  generally  speaking,  the 

best  conductors. 

It  is  thus  found  that  metals  are  unequally  good  conductors  of  heat, 
and  that  they  may  be  arranged  in  the  following  order,  beginning  with 
the  best  conductors: — Silver,  copper,  gold,  brass,  tin,  iron,  lead, 
platinum,  bismuth. 

In  both  these  experiments  we  must  beware  of  attempting  to 
measure  conductivity  by  the  quickness  with  which  the  melting 
advances.  This  quickness  may  be  simply  an  indication  of  small 
specific  heat.1 

}  330.  Conducting  Power  of  Metals. — Metals,  though  differing  con- 
siderably one  from  another,  are  as  a  class  greatly  superior  in  con- 
ductivity to  other  substances,  such  as  wood,  marble,  brick.  This 
explains  several  familiar  phenomena.  If  the  ha,nd  be  placed  upon  a 
metal  plate  at  the  temperature  of  10°  G,  or  plunged  into  mercury  at 
this  temperature,  a  very  marked  sensation  of  cold  is  experienced. 
This  sensation  is  less  intense  with  a  plate  of  marble  at  the  same 
temperature,  and  still  less  with  a  piece  of  wood.  The  reason  is  that 
the  hand,  which  is  at  a  higher  temperature  than  the  substance  to 
which  it  is  applied,  gives  up  a  portion  of  its  heat,  which  is  conducted 
away  by  the  substance,  and  consequently  a  larger  portion  of  heat  is 
parted  with,  and  a  more  marked  sensation  of  cold  experienced,  in  the 
case  of  the  body  of  greater  conducting  power. 

331.  Davy  Lamp. — The  conducting  power  of  metals  explains  the 
curious  property  possessed  by  wire-gauze  of  cutting  off  a  flame.  If, 
for  example,  a  piece  of  wire-gauze  be  placed  above  a  jet  of  gas,  the 
flame  is  prevented  from  rising  above  the  gauze.  If  the  gas  be  first 
allowed  to  pass  through  the  gauze,  and  then  lighted  above,  the  flame 
is  cut  off  from  the  burner,  and  is  unable  to  extend  itself  to  the  under- 
surface  of  the  gauze.  These  facts  depend  upon  the  conducting  power 

1  Strictly  speaking,  small  specific  heat  per  unit  volume,  not,  as  usual,  per  unit  mass. 


418 


CONDUCTION   OF   HEAT. 


of  metallic  gauze,  in  virtue  of  which  the  heat  of  the  flame  is  rapidly 
dissipated  at  the  points  of  contact,  the  result  being  a  diminution  of 

temperature  sufficient 
to  prevent  ignition. 

This  property  of 
metallic  gauze  has 
been  turned  to  ac- 
count for  various  pur- 
poses, but  its  most 
useful  application  is 
in  the  safety- lamp  of 

Fig.  295.-Action  of  Wire-gauze  on  Flame.  Sir  Humphrey  Davy. 

It  is  well   known 

that  a  gas  called  fire-damp  is  often  given  off  in  coal-mines.  It  is  a 
compound  of  carbon  and  hydrogen,  and  is  a  large  ingredient  in  ordi- 
nary coal-gas. 

This  fire-damp,  when  mixed  with  eight  or  ten  times  its  volume  of 
air,  explodes  with  great  violence  on  coming  in  contact  with  a  lighted 

body.  To  obviate  this  danger,  Davy  in- 
vented the  safety-lamp,  which  is  an  ordi- 
nary lamp  with  the  flame  inclosed  by 
wire -gauze.  The  explosive  gases  pass 
through  the  gauze,  and  burn  inside  the 
lamp,  in  such  a  manner  as  to  warn  the 
miner  of  their  presence;  but  the  flame  is 
unable  to  pass  through  the  gauze. 
>  -332.  Various  Applications. — The  know- 
ledge of  the  relative  conducting  powers 
of  different  bodies  has  several  important 
practical  applications. 

In  cold  countries,  where  the  heat  pro- 
duced in  the  interior  of  a  house  should  be 
as  far  as  possible  prevented  from  escaping, 
the  walls  should  be  of  brick  or  wood, 
which  have  feeble  conducting  powers.  If 

they  are  of  stone,  which  is  a  better  conductor,  a  greater  thickness 
is  required.  Thick  walls  are  also  useful  in  hot  countries  in  resisting 
the  power  of  the  solar  rays  during  the  heat  of  the  day. 

We  have  already  alluded  (§  224)  to  the  advantage  of  employing 
fire-brick,  which  is  a  bad  conductor,  as  a  lining  for  stoves. 


Fig.  296.— Davy  Lamp. 


DETERMINATION   OF  CONDUCTIVITY. 


419 


The  feeble  conducting  power  of  brick  has  led  to  its  employment 
in  the  construction  of  ice-houses.  These  are  round  pits,  generally 
from  6  to  8  yards  in  diameter  at 
top,  and  somewhat  narrower  at 
the  bottom,  where  there  is  a  grat- 
ing to  allow  the  escape  of  water. 
The  inside  is  lined  with  brick,  and 
the  top  is  covered  with  straw, 
which,  as  we  shall  shortly  see,  is 
a  bad  conductor.  In  order  to 
diminish  as  much  as  possible  the 
extent  of  surface  exposed  to  the 
action  of  the  air,  the  separate 
pieces  are  dipped  in  water  before 
depositing  them  in  the  ice-house, 
and,  by  their  subsequent  freezing 
together,  a  solid  mass  is  produced, 
capable  of  remaining  umnelted 
for  a  very  long  time. 
0  333.  Experimental  Determina- 
tion of  Conductivity. — Several  ex- 
perimenters have  investigated  the  conductivity  of  metals,  by  keeping 
one  end  of  a  metallic  bar  at  a  high  temperature,  and,  after  a  sufficient 
lapse  of  time,  observing  the  permanent  temperatures  assumed  by 
different  points  in  its  length. 

If  the  bar  is  so  long  that  its  further  end  is  not  sensibly  warmer 
than  the  surrounding  air,  and  if,  moreover,  Newton's  law  of  cooling 
be  assumed  true  for  all  parts  of  the  surface,  and  all  parts  of  a  cross 
section  be  assumed  to  have  the  same  temperature,  the  conductivity 
being  also  assumed  to  be  independent  of  the  temperature,  it  is  easily 
shown  that  the  temperatures  of  the  bar  at  equidistant  points  in  its 
length,  beginning  from  the  heated  end,  must  exceed  the  atmospheric 
temperature  by  amounts  forming  a  decreasing  geometric  series. 
Wiedemann  and  Franz,  by  the  aid  of  the  formula  to  which  these 
assumptions  lead^computed  the  relative  conducting  powers  of  several 

1  If  p  and  s  denote  the  perimeter  and  section  of  the  bar,  Tc  the  conductivity,  and  h  the 
coefficient  of  emission  of  the  surface  at  the  temperature  v,  the  heat  emitted  in  unit  time 
from  the  length  5x  is  hvpdx,  if  we  assume  as  our  zero  of  temperature  the  tempera- 
ture of  the  surrounding  air.  But  the  heat  which  passes  a  section  is  s Tc  — ,  and  that 

dx 


Fig.  297. — Ice-house. 


420  CONDUCTION   OF   HEAT. 

of  the  metals,  from  experiments  on  thin  bars,  which  were  steadily 
heated  at  one  end,  the  temperatures  at  various  points  in  the  length 
being  determined  by  means  of  a  thermo-electric  junction  clamped  to 
the  bar.  The  following  were  the  results  thus  obtained: — 

RELATIVE  CONDUCTING  POWERS. 
Silver 100  Steel, ,12 


Copper, 77'6 

Gold, 53-2 

Brass, 33 

Zinc, 19'9 

Tin, 14-5 


Iron, 11-9 

Lead, 8-5 

Platinum, 82 

Palladium, 6' 3 

Bismuth, 1'9 


The  absolute  conductivity  of  wrought  iron  was  investigated  with 
great  care  by  Professor  J.  D.  Forbes,  by  a  method  which  avoided 
some  of  the  questionable  assumptions  above  enumerated.  The  end 
of  the  bar  was  heated  by  a  bath  of  melted  lead  kept  at  a  uniform 
temperature,  screens  being  interposed  to  protect  the  rest  of  the  bar 
from  the  heat  radiated  by  the  bath.  The  temperatures  at  other 
points  were  observed  by  means  of  thermometers  inserted  in  small 
holes  drilled  in  the  bar,  and  kept  in  metallic  contact  by  fluid  metal. 
In  order  to  determine  the  loss  of  heat  by  radiation  at  different  tem- 
peratures, a  precisely  similar  bar,  with  a  thermometer  inserted  in  it, 
was  raised  to  about  the  temperature  of  the  bath,  and  the  times  of 
cooling  down  through  different  ranges  were  noted. 

The  conductivity  of  one  of  the  two  bars  experimented  on,  varied 
from  -01337  at  0°  C.  to  "00801  at  275°  C.,  and  the  corresponding 
numbers  for  the  other  bar  were  -00992  and  '00724,  the  units  being 
the  foot,  the  minute,  the  degree  (of  any  scale),  and  the  foot-degree1 
(of  the  same  scale).  In  both  instances,  the  conductivity  decreased 
regularly  with  increase,  of  temperature. 

Absolute  determinations  have  also  been  made  of  the  conductivity 
of  the  soil  or  rock  at  three  localities  in  or  near  Edinburgh,  by  Pro- 

which  passes  a  section  further  on  by  the  amount  5x  is  less  by  the  amount  s&  _— V-  8x;  and 

d  9& 

this  difference  must  equal  the  amount  emitted  from  the  intervening  portion  of  the  surface. 
Hence  we  have  the  equation  — ^  =  — ^  v,  the  integral  of  which  for  the  case  supposed  is 

tl  *C  /C  8 

v^ 

X  V  7— 

v=Ve         **, 

V  denoting  the  temperature  at  the  heated  end. 
1  See  §§339,  340. 


CONDUCTING   POWERS   OF   LIQUIDS.  421 

fessor  Forbes  and  Sir  W.  Thomson.  When  expressed  in  terms  of  the 
above  units,  they  are — 

Trap  rock  of  Calton  Hill, '000263 

Sand  of  Experimental  Garden,         ....     '000169 
Sandstone  of  Craigleith  Quarry,       ....     '000689 

These  determinations  were  derived  from  observations  on  the  tem- 
perature of  the  soil  as  indicated  by  thermometers  having  their  bulbs 
buried  at  depths  of  from  3  to  24  feet.  The  annual  range  of  tem- 
perature diminished  rapidly  as  the  depth  increased  ;  and  this  diminu- 
tion of  range  was  accompanied  by  a  retardation  of  the  times  of 
maximum  and  minimum.  To  deduce  the  conductivity,1  it  was 
necessary  fir.st  to  reduce  the  annual  variation  of  each  thermometer 
to  the  sum  of  a  number  of  terms  each  of  which  would  express  a 
simple  harmonic  variation  or  simple  vibration  (§  53 A),  the  most 
important  of  these  being  the  annual  term,  which  represents  a  simple 
vibration  whose  period  is  a  year.  By  comparing  the  amplitudes  of 

this  term  at  two  different  depths,  we  obtain  the  value  of  -,  k  de- 
noting conductivity,  and  c  capacity  per  unit  volume;  and  another 
independent  determination  of  the  same  element  is  obtained  by  com- 
paring the  epochs,  in  other  words  by  noting  the  retardation  of  phase 
which  this  term  undergoes.  The  value  of  c  was  determined  by  direct 
experiments  conducted  by  Regnault,  and  lastly,  this  value  multi- 
plied by  —  gave  the  conductivity  Jc. 

,  334.  Conducting  Powers  of  Liquids. — With  the  exception  of  mer- 
cury and  other  melted  metals,  liquids  are  exceedingly  bad  conduc- 
tors of  heat.  This  can  be  shown  by  heating  the  upper  part  of  a 
column  of  liquid,  and  observing  the  variations  of  temperature  below. 
These  will  be  found  to  be  scarcely  perceptible,  and  to  be  very  slowly 
produced.  If  the  heat  were  applied  below  (Fig.  298),  we  should  have 
the  process  called  convection  of  heat;  the  lower  layers  of  liquid  would 
rise  to  the  surface,  and  be  replaced  by  others  which  would  rise  in 
their  turn,  thus  producing  a  circulation  and  a  general  heating  of  the 
liquid.  On  the  other  hand,  when  heat  is  applied  above,  the  expanded 
layers  remain  in  their  place,  and  the  rest  of  the  liquid  can  be  heated 
by  conduction  and  radiation  only. 

1  The  process  of  reduction  is  fully  explained,  both  theoretically  and  practically,  in  two 
papers  (by  Sir  W.  Thomson  and  the  Editor  of  this  work)  in  the  Trans.  Roy.  Soc.  Edin. 
1860. 


422 


CONDUCTION    OF  HEAT. 


The  following  experiment  is  one  instance  of  the  very  feeble  con- 
ducting power  of  water.     A  piece  of  ice  is  placed  at  the  bottom  of  a 


Fig.  298.— Liquid  heated  from  below. 


Fig.  299.— Boiling  of  Water  over  Ice. 


glass  tube  (Fig.  299),  which  is  then  partly  filled  with  water ;  heat  is 
applied  to  the  middle  of  the  tube,  and  the  upper  portion  of  the  water 
is  readily  raised  to  ebullition,  without  melting  the  ice  below. 

335.  Measure  of  the  Conducting  Power  of  Water. — The  power  of 
conducting  heat  possessed  by  water,  though  very  small,  is  yet  capable 
of  measurement.  This  was  established  by  Despretz  by  the  following 
experiment.  He  took  a  cylinder  of  wood  (Fig.  300)  about  a  yard  in 
height  and  eight  inches  in  diameter,  which  was  filled  with  water.  In 
the  side  of  this  cylinder  were  arranged  twelve  thermometers  one  above 
another,  their  bulbs  being  all  in  the  same  vertical  through  the  middle 
of  the  liquid  column.  On  the  top  of  the  liquid  rested  a  metal  box, 
which  was  filled  with  water  at  100°,  frequently  renewed  during  the 
course  of  the  experiment  Under  these  circumstances  Despretz 
observed  that  the  temperature  of  the  thermometers  rose  gradually, 
and  that  a  long  time — about  30  hours — was  required  before  the 
permanent  state  was  assumed.  Their  permanent  differences,  which 
formed  a  decreasing  geometric  series,  were  very  small,  and  were 
inappreciable  after  the  sixth  thermometer. 


CONDUCTING  POWER  OF  WATER. 


423 


The  increase  of  temperature  indicated  by  the  thermometers  might 
be  attributed  to  the  heat  received  from  the  sides  of  the  cylinder, 
though  the  feeble  conducting  power  of  wood  renders  this  idea  some- 


Fig.  300. — Despretz's  Experiment. 

what  improbable.  But  Despretz  observed  that  the  temperature  was 
higher  in  the  axis  of  the  cylinder  than  near  the  sides,  which  proves 
that  the  elevation  of  temperature  was  due  to  the  passage  of  heat 
downwards  through  the  liquid. 

From  recent  experiments  by  Professor  Guthrie,1  it  appears  that 
water  conducts  better  than  any  other  liquid  except  mercury. 

336.  Conducting  Power  of  Gases. — Of  the  conducting  powers  of 
gases  it  is  almost  impossible  to  obtain  any  direct  proofs,  since  it  is 
exceedingly  difficult  to  prevent  the  interference  of  convection  and 
direct  radiation.  However,  we  know  at  least  that  they  are  exceed- 
ingly bad  conductors.  In  fact,  in  all  cases  where  gases  are  inclosed 
in  small  cavities  where  their  movement  is  difficult,  the  system  thus 
formed  is  a  very  bad  conductor  of  heat.  This  is  the  cause  of  the 
feeble  conducting  powers  of  many  kinds  of  cloth,  of  fur,  eider-down, 
felt,  straw,  saw-dust,  &zc.  Materials  of  this  kind,  when  used  as 
articles  of  clothing,  are  commonly  said  to  be  warm,  because  they 

hinder  the  heat  of  the  body  from  escaping.    If  a  garment  of  eider-down 

i 

1  B.  A.  Report,  1868,  and  Trans.  R.  S.  1869. 


CONDUCTION   OF  HEAT. 

or  fur  were  compressed  so  as  to  expel  the  greater  part  of  the  air,  and 
to  reduce  the  substance  to  a  thin  sheet,  it  would  be  found  to  be  a 
much  less  warm  covering  than  before,  having  become  a  better  con- 
ductor. We  thus  see  that  it  is  the  presence  of  air  which  gives  these 
substances  their  feeble  conducting  power,  and  we  are  accordingly 
justified  in  assuming  that  air  is  a  bad  conductor  of  heat. 
,  .  337.  Norwegian  Stove. — A  curious  application  of  the  bad  con- 
ducting power  of  felt  is  occasionally  to  be  seen  in  the  north  of 
Europe,  in  a  kind  of  self-acting  cooking-box.  This  is  a  box  lined 
inside  with  a  thick  layer  of  felt,  into  which  fits  a  metallic  dish  with 


Fig.  301.— Norwegian  Cooking  box. 

a  cover.  The  dish  is  then  covered  with  a  cushion  of  felt,  so  as  to  be 
completely  surrounded  by  a  substance  of  very  feeble  conducting 
power.  The  method  of  employing  the  apparatus  is  as  follows : — The 
meat  which  it  is  desired  to  cook  is  placed  along  with  some  water  in 
the  dish,  the  whole  is  boiled  for  a  short  time,  and  then  transferred 
from  the  fire  to  the  box,  where  the  cooking  is  completed  without  any 


CONDUCTIVITY   OF  HYDROGEN. 


425 


farther  application  of  heat  The  isolating  power  of  the  stuffing  of 
the  box,  as  far  as  regards  heat,  is  exceedingly  great ;  in  fact,  it  may 
be  shown  that  at  the  end  of  three  hours 
the  temperature  of  the  water  has  fallen  by 
only  about  10°  or  15°  C.,  and  has  accord- 
ingly remained  during  all  that  time  suffi- 
ciently high  to  conduct  the  operation  of 
cooking. 

^__— —  O 

338.  Conductivity  of  Hydrogen. — The 
conducting  power  of  hydrogen  is  much 
superior  to  that  of  the  other  gases — a  fact 
which  agrees  with  the  view  entertained 
by  chemists,  that  this  gas  is  the  vapour 
of  a  metal.  The  good  conductivity  of 
hydrogen  is  shown  by  the  following  expe- 
riments :  — 

1.  Within   a   glass   tube  (Fig.    302)   is 
stretched  a  thin  platinum  wire,  which  is 
raised  to  incandescence  by  the  passage  of 
an  electric  current.     When  air,  or  any  gas 
other  than   hydrogen,   is   passed    through 
the    tube,    the    incandescence    continues, 
though  with  less  vividness  than  in  vacuo ; 
but  it  disappears  as  soon  as  hydrogen  is 
employed. 

2.  A  thermometer  is  placed  at  the  bot- 
tom of  a  vertical  tube,  and  heated  by  a 
vessel  containing  boiling  water  which  is 
placed  at  the  top  of  the  tube.     The  tube 
is  exhausted   of  air,   and   different  gases 
are  successively  admitted.      In   each  case 
the  indication  of  the  thermometer  is  found 
to  be  lower  than  for  vacuum,  except  when 
the  gas  is  hydrogen.     With  this  gas,  the 

difference  is  in  the  opposite  direction,  showing  that  the  diminution 
of  radiation  has  been  more  than  compensated  by  the  conducting 
power  of  the  hydrogen. 


L    V 


Fig.  302.— Cooling  by  Contact 
of  Hydrogen 


CHAPTER    XXXI. 


CALOIUMETRY. 


.  339.  Quantities  of  Heat. — Calorirnetry  consists  in  the  measurement 
of  quantities  of  heat.  This  can  be  effected  without  making  any 
assumption  as  to  what  heat  is.  It  merely  presupposes  the  power  of 
identifying  equal  quantities. 

If  two  different  thermic  actions,  of  which  one  may  be  friction,  and 
the  other  combustion,  when  separately  applied  to  the  heating  of  a 
pound  of  water,  raise  its  temperature  in  each  case  from  0°  C.  to  1°  G, 
we  say  that  the  water  receives  equal  quantities  of  heat  in  both  cases ; 
and  the  quantity  of  heat  required  to  raise  m  pounds  of  water  from 
0°  C.  to  1°  C.  would  be  m  times  as  great. 

In  order  to  test  whether  the  quantity  of  heat  required  to  raise  the 
temperature  of  a  pound  of  water  by  1°  C.  is  the  same  at  all  initial 
temperatures  of  the  water,  we  may  employ  the  method  of  mixtures. 
Let  us,  for  example,  mix  3  Ibs.  of  water  at  15°  with  5  Ibs.  at  35°,  and 
observe  the  temperature  of  the  mixture.  If  this  temperature  be 
denoted  by  x,  the  3  Ibs.  have  risen  through  the  range  x —  15,  arid  the 
5  Ibs.  have  fallen  through  the  range  35  —  x.  If  a  rise  or  fall  of  1° 
involves  the  same  gain  or  loss  of  heat  at  all  temperatures,  the  quan- 
tity of  heat  gained  by  the  3  Ibs.  may  be  represented  by  3  (x  — 15), 
and  the  heat  lost  by  the  5  Ibs.  will  be  represented  by  5  (35  —  x).  But 
what  the  one  has  gained  the  other  has  lost;  we  have  therefore 

3(«-15)=5  (35-*), 
whence 

<c  =  27'5. 

Calculation,  based  on  this  principle,  is  found  to  agree  very  accurately 
with  experiment  up  to  about  40°  C.  We  may  therefore  define  the 
unit  of  heat  as  the  quantity  of  heat  required  to  raise  the  temperature 
of  unit  mass  of  water  1°,  between  the  limits  0°  C.  and  40°  C. 


THERMAL    CAPACITY. 

Several  different  units  of  beat  are  employed,  all  having  reference 
to  pure  water  between  these  limits  of  temperature. 

The  gramme-degree  (Centigrade)  is  the  quantity  of  heat  required 
to  raise  a  gramme  of  water  1°  (Centigrade). 

The  kilogramme-degree  (Centigrade)  is  the  heat,  required  to  raise 
a  kilogramme  of  water  1°  (Centigrade).  It  is  sometimes  called  the 
calorie. 

The  pound-degree  (Fahrenheit  or  Centigrade)  is  the  heat  required 
to  raise  a  pound  avoirdupois  of  water  1°. 

The  foot-degree  (Fahrenheit  or  Centigrade)  is  the  heat  required  to 
raise  a  cubic  foot  of  water  1°. 

We  shall  briefly  describe  in  this  chapter  three  of  the  most  important 
applications  of  calorimetry : — 

1.  In  connection  with  changes  of  temperature  (specific  heat) ; 

2.  In  connection  with  change  of  state  (latent  heat) ; 

3.  In  connection  with  chemical  actions  (heat  of  combination). 
340.  Thermal  Capacity — Specific  Heat. — The  thermal  capacity  of  a 

body  is  the  quantity  of  heat  required  to  raise  the  temperature  of  the 
body  one  degree.  It  is  numerically  equal  to  the  mass  or  volume  of 
water  (according  to  the  unit  of  heat  employed)  which  would  be  raised 
one  degree  by  the  same  quantity  of  heat. 

The  specific  heat  of  a  substance  is  the  thermal  capacity  of  unit  mass 
of  the  substance,  or,  more  simply,  is  the  ratio  of  the  thermal  capacity 
of  the  substance  to  that  of  an  equal  weight  of  water.  It  is  obviously 
independent  of  the  unit  of  mass  and  scale  of  temperature  adopted. 

It  is  sometimes  necessary  to  consider  the  thermal  capacity  of  unit 
volume  of  a  substance.1  This  will  be  the  same  as  the  ratio  of  the 
thermal  capacity  of  the  substance  to  that  of  an  equal  volume  of  water, 
if  we  employ  as  unit  of  heat  the  heat  required  to  raise  unit  volume 
of  water  one  degree.  In  discussions  relating  to  conduction,  if  the 
foot  be  made  the  linear  unit,  the  unit  of  heat  employed  should  be  the 
heat  required  to  raise  a  cubic  foot  of  water  one  degree.  Thermal 
capacity  per  unit  volume  is,  like  thermal  capacity  per  unit  mass, 
independent  of  the  units  employed,  provided  they  are  employed 
consistently. 

Experiment  shows  that  nearly  equal  quantities  of  heat  are  required 
to  raise  a  body  through  1°  at  ail  temperatures  between  0°  C.  and 

1  This  is  evidently  equal  to  specific  heat  multiplied  by  density;  that  is,  to  the  thermal 
capacity  of  unit  mass  multiplied  by  the  number  of  units  of  mass  which  are  contained  in  a 
unit  of  volume. 


428' 


CALOR1METRY. 


100°  C.  ;  in  other  words,  specific  heat  varies  but  very  slightly  with 
temperature  between  these  limits.  The  quantity  of  heat  which  must 
be  added  to  or  taken  from  a  body  to  raise  or  lower  its  temperature 
by  T°  will  therefore  be  proportional  to  T,  and  will,  in  fact,  be  given 
by  the  formula 


where  W  denotes  the  weight  of  the  body,  and  S  its  specific  heat.     The 
product  WS  is  the  thermal  capacity  of  the  whole  body. 

The  specific  heats  of  different  substances  differ  very  widely  from 
one  another.  This  is  easily  tested  by  the  following  experiment.1 

A  number  of  balls,  of  different 
materials  and  of  equal  weight, 
are  heated  to  the  same  tempera- 
ture —  suppose  200°  —  and  placed 
upon  a  wax  disc.  Each  of  the 
balls  gives  up  part  of  its  heat 
to  the  wax,  causing  it  to  melt, 
and  thus  making  a  hole  through 
which  the  ball  finally  drops. 
The  balls  of  the  greatest  specific 
heat  drop  through  first;  thus 
the  iron  ball  falls  before  the 
copper,  the  copper  ball  before 
the  tin,  &c.,  while  the  balls  of 
lead  and  bismuth  are  much 
slower  in  their  action,  and,  if 
the  disc  be  moderately  thick,  never  get  through  at  all. 

As  another  example  we  may  take  the  following  experiment,  which 
serves  to  show  the  great  difference  between  the  specific  heat  of  mer- 
cury and  that  of  water. 

A  kilogramme  of  water  at  10°  and  a  kilogramme  of  mercury  at  100° 
are  poured  into  the  same  vessel  and  well  shaken  together.  The  tem- 
perature of  the  whole  is  then  found  to  be  about  13°,  the  water  having 
gained  3  units  of  heat,  which  have  been  furnished  by  the  mercury, 
and  this  loss  has  caused  the  temperature  of  the  latter  to  fall  through 

1  Critically  considered,  this  experiment  gives  -undue  advantage  to  the  balls  of  heavy 
material,  because  they  have  not  to  make  such  large  holes  for  themselves  as  the  lighter  ones, 
in  order  to  get  through.  If  the  balls  are  all  made  of  the  same  size,  we  have  a  pretty  fair 
hest  of  their  thermal  capacities  per  unit  volume. 


Fig.  303.— Balls  Melting  their  way  through  Disc. 


SPECIFIC  HEAT.  429 

57°.     Thus  we  see  that  the  specific  heat  of  mercury  is  about  J_  or  ^ 

87         29> 

that  of  water  being  unity.1 

In  order  to  determine  this  element  exactly,  a  number  of  minute 
precautions  are  required;  in  fact,  the  experiment  just  described  is  to 
be  regarded  merely  as  a  means  of  readily  exhibiting  the  difference 
between  the  specific  heats  of  the  two  bodies.  The  methods  of  accur- 
ately determining  specific  heats  are  various ;  we  shall  describe  only 
two  of  them. 

341.  Method  by  Fusion  of  Ice. — A  hole  is  scooped  in  a  solid  block 
of  ice,  and  a  lid  of  the  same  substance  is  fitted  over  it.  A  body  of 
weight  W  is  heated  to  a  temperature  T  and 
placed  in  the  hole,  which  is  immediately 
covered  with  the  lid.  The  body,  in  cooling 
down  to  0°,  gives  off  a  quantity  of  heat  which 
melts  some  of  the  ice.  The  water  thus  ob- 
tained is  wiped  up  with  cotton  wool,  which 
is  then  weighed,  having  previously  been 


fat 


weighed  dry.  If  the  weight  of  water  thus  Fig.  3o4.-ice-biock  calorimeter. 
found  be  denoted  by  m,  the  quantity  of  heat 

necessary  to  produce  it  is,  by  §  228,  79  m.  But  this  heat  is  supplied 
by  the  body,  and  has  produced  in  it  a  fall  of  temperature  amount- 
ing to  T°,  which  correspond  to  WST  units  of  heat,  S  being  the  spe- 
cific heat  of  the  body.  Hence  we  have  WST=79  m,  whence  S  = 

79m 
\VT' 

This  method  is  due  to  the  Swedish  philosopher  Wilke,  and  is  dif- 
ficult of  application  in  our  climate.  An  apparatus,  based  on  the  same 
principle,  and  called  the  ice-calorimeter,  was  employed  by  Lavoisier 
and  Laplace,  and  has  recently  been  improved  by  Bunsen  (Phil.  Mag. 
March,  1871). 

342.  Method  of  Mixtures — Its  Principle. — The  method  of  mixtures 
resembles  the  experiment  which  we  have  already  described  as  illus- 
trating the  difference  between  the  specific  heats  of  mercury  and  water.2 

1  The  specific  heat  of  mercury  is  almost  exactly  •£$;  see  table  §  344. 

2  If  weights  w,  vf  of  two  substances  whose  specific  heats  are  s,  s  and  temperatures  t,  f, 
are  mixed,  the  substances  being  supposed  not  to  act  chemically  on  one  another,  and  no 
heat  being  gained  or  lost  externally,  it  is  easily  shown  that  the  temperature  of  the  mixture 

will  be 

wst  +  w  s' t' 

ws  +  w  s'  ' 

and,  by  appending  additional  terms  to  numerator  and  denominator,  the  formula  becomes 
applicable  to  a  mixture  of  any  number  of  substances. 


430  CALORIMETKY. 

A  body  of  a  known  weight  W  is  raised  to  a  fixed  temperature  T, 
and  then  plunged  into  a  quantity  of  water  of  weight  W  and  tem- 
perature t,  which  is  contained  in  a  copper  vessel  called  a  calorimeter. 
As  T  is  supposed  to  exceed  t,  the  water  gains  in  temperature  by  the 
immersion  of  the  body,  and  finally  attains  a  maximum  temperature  Q, 
,  which  is  noted.  In  the  change  from  t  to  0,  the  water  has  gained  a 
quantity  of  heat  equal  to  W  (0  —  t),  and  the  body  immersed  has  lost 
a  quantity  equal  to  W  x  (T  —  0;,  x  being  the  specific  heat  required. 
Equating  these  two  quantities,  we  have 

W  (e-t)=Wx(T-e),  (a) 

whence 

*  =  W'J*Z*) 
W  (T-6)' 

343.  Sources  of  Error. — Such  is  the  principle  of  the  method  of 
mixtures ;  but,  upon  closer  examination,  it  will  easily  be  seen  that 
equation  (a),  for  various  reasons,  must  be  regarded  as  only  approxi- 
mate. 

I.  The  equation  assumes  that  the  only  exchange  of  heat  is  between 
the  body  and  the  water,  which  is  not  actually  the  case. 

1.  The  body  is  often  contained  in  an  envelope  which  cools  along 
with  it,  and  thus  furnishes  part  of  the  heat  given  up. 

2.  The  heat  of  the  body  is  not  given  up  exclusively  to  the  water 
in  the  calorimeter,  but  partly  to  the  calorimeter  itself,  to  the  thermo- 
meter, and  to  such  other  instruments  as  may  be  employed  in  the 
experiment,  as,  for  instance,  a  rod  to  stir  the  liquid  for  the  purpose 
of  establishing  uniformity  of  temperature  throughout  it. 

The  equation  for  the  most  general  case  can  easily  be  written  down. 
We  have  only  to  express  that  the  quantity  of  heat  given  up  by  the 
body  and  its  envelope  is  equal  to  that  gained  by  the  water,  the 
calorimeter,  the  thermometer,  and  the  rod. 

Let  W  denote  the  weight  of  the  body,  T  its  initial  temperature, 
x  its  specific  heat,  m  the  weight  of  the  envelope,  a  its  specific  heat, 
W'  the  weight  of  the  water  in  the  calorimeter,  w  the  weight  of  the' 
calorimeter,  c  its  specific  heat,  w  the  weight  of  the  glass  of  the  ther- 
mometer, c'  its  specific  heat,  w"  the  weight  of  the  mercury,  c"  its 
specific  heat,  w'"  the  weight  of  the  rod  for  stirring,  c"  its  specific 
heat,  Q  the  final  temperature. 

Under  these  circumstances  we  evidently  have  the  equation 

Wx    T- 


METHOD   OF  MIXTURES.  431 

whence  we  find 


(0-Q -ma  (T-0) 
W(T-0) 

The  above  equation  is  the  general  type  of  all  equations  which  occur 
in  questions  of  this  kind;  the  only  difference  that  can  arise  is  in  the 
number  of  the  terms,  since  each  term  represents  a  quantity  of  heat 
gained  or  lost  by  one  of  the  bodies  employed  in  the  experiment. 

In  the  above  expression  for  x,  the  coefficient  of  (0  —  t)  is  what  is  called 
the  water-equivalent  of  the  calorimeter,1  representing,  in  fact,  a  mass 
of  water  such  that,  supposing  it  to  receive  exclusively  all  the  heat 
given  up  in  the  experiment,  a  thermometer  placed  in  it  would  indi- 
cate the  variation  of  temperature  actually  observed.  Among  the 
elements  which  enter  this  coefficient  are  the  specific  heat  of  the 
material  of  the  calorimeter  and  of  the  rod  for  stirring;  these  are 
generally  made  of  brass,  and  their  specific  heat  may  be  considered  as 
known  with  sufficient  approximation  from  previous  experiments. 
The  two  terms  connected  with  the  thermometer  may  be  directly 
determined  by  a  previous  experiment  with  a  body  whose  specific  heat 
is  known. 

II.  The  calorimeter,  when  heated  by  the  body  immersed  in  the 
liquid,  loses  a  certain  quantity  of  heat  by  radiation,  which  must  be 
taken  into  account  if  we  wish  to  obtain  a  rigorous  result.  For  this 
purpose  a  very  simple  method  of  compensation  was  proposed  by 
Rumford.  It  consists  in  lowering  the  initial  temperature  of  the 
calorimeter  below  that  of  the  surrounding  air  by  a  number  of  degrees 
equal  to  the  excess  of  the  final  temperature  above  that  of  the  sur- 
rounding air,  which  may  easily  be  effected  by  means  of  a  previous 
trial.  In  this  case  the  experiment  may  be  divided  into  two  parts, 
during  the  first  of  which  the  calorimeter  gains  heat  by  radiation, 
while  during  the  second  it  loses  heat  by  the  same  process.  As  the 
difference  of  temperature  between  the  calorimeter  and  the  air  is 
the  same  in  both  cases,  we  may  consider  the  quantities  of  heat  as 
equal.  The  compensation,  however,  is  not  exact,  since  the  two 
periods  are  of  unequal  length,  and  accordingly  the  method  adopted 
by  most  investigators  has  been  different.  This  consists  in  deter- 
mining the  constant  in  the  expression  for  the  rate  of  cooling  (§  307), 
and  employing  it  in  the  direct  calculation  of  the  number  of  degrees 
lost  by  radiation.  In  order  to>  effect,  this  calculation,  instead  of  sup- 

1  This  is  only  another  name^for  the  thermal  capacity  of  th*  calorimeter  and  its  contents. 


CALORIMETRY. 

posing  the  variation  of  temperature  to  be  continuous,  they  divide 
the  entire  length  of  the  experiment  into  a  number  of  parts,  during 
each  of  which  they  suppose  the  excess  constant,  and  this  method  of 
approximation  is  always  found  to  be  sufficient. 

III.  The  calorimeter  loses  heat  also  by  the  supports  on  which  it 
rests.  This  source  of  error  can  never  be  entirely  removed,  but  it  may 
easily  be  rendered  so  small  as  to  be  quite  insensible.  This  is  effected 
by  making  the  supports  of  some  substance  which  is  a  very  bad  con- 
ductor, and  by  diminishing  the  extent  of  surface  of  contact  between 
them  and  the  calorimeter. 

Finally,  we  should  ascertain  carefully  the  initial  temperature  of 
the  body,  and  provide  against  any  fall  of  temperature  in  transferring 
it  from  the  place  of  heating  to  the  calorimeter. 

344.  Regnault's  Apparatus. — The  subject  of  specific  heat,  both  for 
solids  and  liquids,  has  been  investigated  with  great  care  by  Regnault, 
who  employed  for  that  purpose  an  apparatus  in  which  the  advantages 


Fig.  305. — Regnault's  Apparatus. 


of  convenience  and  precision  are  combined.  The  body  whose  specific 
heat  is  required  is  divided  into  small  fragments,  which  are  placed  in 
a  cylindrical  basket  G  of  very  fine  brass  wire.  This  basket  is  sus- 
pended inside  the  steamer  A,  the  suspending  thread  being  fixed  by 


REGNAULT'S  APPARATUS.  433 

the  cork  K,  through  which  passes  the  stem  of  a  thermometer,  the 
reservoir  of  which  rests  in  a  small  tube  in  the  centre  of  the  basket, 
and  made  of  the  same  material.  The  steamer  is  a  double  cylinder, 
the  inside  compartment  B  of  which  is  filled  with  steam  supplied  by 
the  boiler  V,  and  afterwards  conducted  by  the  tube  D  into  a  con- 
denser. In  the  bottom  of  the  steamer  is  a  sliding-door  E,  which  can 
be  drawn  out  when  required.  The  outside  compartment  C  is  filled 
with  air,  to  prevent  the  temperature  of  the  inside  from  cooling  by 
contact  with  the  air  outside. 

This  entire  apparatus  rests,  by  means  of  a  sheet  of  cork,  upon  a 
hollow  inetal  vessel  MN,  filled  with  water,  the  vertical  face  of  which 
N  serves  as  a  screen  to  protect  the  calorimeter  against  the  heat  of  the 
fire.  The  calorimeter  itself  is  a  vessel  of  very  thin  polished  brass,  rest- 
ing upon  silk  threads  stretched  across  the  bottom  of  a  larger  vessel. 
This  latter  rests  by  three  points  upon  a  small  wooden  sled,  which 
runs  smoothly  along  a  rail.  The  thermometer  for  measuring  the 
temperature  of  the  water  in  the  calorimeter  is  carried  by  a  support 
attached  to  the  sled.  After  this  explanation  of  the  details,  we  pro- 
ceed to  indicate  the  course  of  an  experiment. 

The  body  is  placed  in  the  basket,  introduced  into  the  steamer,  and 
there  exposed  to  the  action  of  the  steam  which  is  admitted  from  the 
boiler.  During  this  part  of  the  experiment  the  calorimeter  is  kept 
as  far  as  possible  from  the  steamer.  After  the  lapse  of  an  hour  or 
two,  the  thermometer  of  the  steamer  remains  stationary. 

The  calorimeter  is  now  pushed  below  the  sliding-door  E,  the  door 
is  drawn,  and  the  basket  is  rapidly  lowered  into  the  calorimeter, 
which  is  immediately  slid  back  to  its  former  place.  The  basket  is 
moved  about  in  it  for  some  time,  and  the  final  temperature  of  the 
water  is  observed.  Thus  we  have  all  the  elements  required  for  the 
equation  given  above. 

To  determine  the  specific  heats  of  liquids,  a  thin  glass  vessel  is 
employed,  in  which  the  liquid  is  contained,  and  the  effect  pro- 
duced by  this  envelope  is  taken  into  consideration  in  the  general 
equation. 

The  same  method  is  adopted  for  bodies  soluble  in  water,  or  upon 
which  water  has  a  chemical  action,  some  other  liquid  being  in  this 
case  substituted,  as,  for  instance,  oil  of  turpentine.  The  specific  heats 
of  several  substances  are  given  in  the  following  table : — 

28 


434 


CALORIMETRY. 


Water, 

Antimony,  ....  0*05077 

Silver,     .....  0*05601 

Arsenic,       ....  0*08140 

Bismuth,      ....  0'03084 

Cadmium,    ....  0*05669 

Charcoal,     ....  0 '24150 

Copper, 0-09215 

Diamond,     ....  0*14680 

Tin, 0-05623 

Iron, 0-11379 

Iodine,    ,                     ,  G'05412 


SOLIDS. 


LIQUIDS. 


Mercury,      .     , 
Acetic  acid, 
Alcohol  at  36° 


0-03332 

0-6589 

0-6735 


.    i-ooooo 

Brass, 0-09391 

Nickel, 0-10860 

Gold,      .....  0-03244 

Phosphorus,      .     .     .  0*18870 

Platinum,    ....  0-03243 

Lead, 0-03140 

Plum-bago,  ....  0*21800 

Sulphur,       ....  0-20259 

Glass, 0*19768 

Zinc, 0*09555 

Ice, 0-5040 

Benzine, 0*3952 

Ether, 0*5157 

Oil  of  turpentine,    .     .  0*4629 


345.  Great  Specific  Heat  of  Water. — This  table  illustrates  the 
important  fact,  that,  of  all  substances,  water  has  the  greatest  specific 
heat ;  that  is  to  say,  it  absorbs  more  heat  in  warming,  arid  gives  out 
more  heat  in  cooling,  through  a  given  range  of  temperature,  than  an 
equal  weight  of  any  other  substance.  The  quantity  of  heat  which 
raises  a  pound  of  water  from  0°  to  100°  C.  would  suffice  to  raise  a 
pound  of  iron  from  0°  to  about  900°  C.,  that  is  to  a  bright  red  heat; 
and  conversely,  a  pound  of  water  in  cooling  from  100°  to  0°,  gives 
out  as  much  heat  as  a  pound  of  iron  in  cooling  from  900°  to  0°.  This 
property  of  water  is  utilized  in  the  heating  of  buildings  by  hot  water, 
and  in  other  familiar  instances,  such  as  the  bottles  of  hot  water  used 
for  warming  beds,  and  railway  foot- warmers. 

It  is  of  especial  importance  from  the  influence  which  it  exerts  on 
terrestrial  temperatures.  In  fact,  when  we  consider  this  property 
in  conjunction  with  those  which  have  been  indicated  in  §  §  228  and 
247,  we  perceive  that  all  the  thermic  modifications  which  water 
undergoes  are  accompanied  by  the  evolution  or  absorption  of  remark- 
ably large  quantities  of  heat.  If,  for  instance,  the  external  tem- 
perature rises,  much  of  the  additional  heat  is  consumed  in  warming 
the  water,  or  in  converting  it  into  vapour,  or  in  melting  ice.  If,  on 
the  other  hand,  the  temperature  falls,  a  large  amount  of  heat  is  given 
up  to  the  air  by  the  cooling  of  the  water,  the  condensation  of  vapour, 
or  the  formation  of  ice.  In  both  cases,  the  change  of  temperature  is 
greatly  mitigated.  If  the  water  of  the  globe  were  removed,  the  dif- 
ference of  temperature  between  day  and  night,  and  between  summer 
and  winter,  would  very  far  exceed  what  are  observed  at  present. 


SPECIFIC   HEATS   OF   GASES.  435 

*  346.  Dulong  and  Petit's  Law. — Dulong  and  Petit  were  the  first  to 
observe  that  the  product  of  the  specific  heat  of  any  body,  and  what 
is  called  in  chemistry  its  atomic  weight,  is  constant.  This  law  is  of 
considerable  importance,  for  it  shows  that  atoms  require  each  the 
same  amount  of  heat  to  raise  them  through  the  same  number  of 
degrees.  In  fact,  if  w  be  the  atomic  weight  of  a  body,  and  c  its 
specific  heat,  the  quantity  of  heat  necessary  for  a  variation  of  tem- 
perature of  1°  is  civ,  and  it  was  this  product  which  Dulong  and  Petit 
found  to  be  constant. 

347.  Specific  Heats  of  Gases. — The  limits  of  this  treatise  do  not 
permit  us  to  enter  into  the  details  of  the  complicated  processes  by 
which  the  specific  heats  of  gases  have  been  determined.  It  is  neces- 
sary, however,  to  remark  that,  in  the  case  of  gases,  two  kinds  of 
specific  heat  must  be  distinguished. 

1.  Specific  Heat  at  Constant  Pressure. — This  is  the  quantity  of 
heat  required  to  raise  the  temperature  of  unit  weight  of  the  gas  by 
one  degree,  when  the  gas  is  allowed  to  expand  to  such  an  extent  that 
its  pressure  remains  unchanged  during  the  whole  operation  of  heating. 

2.  Specific  Heat  at  Constant  Volume. — This  is  the  amount  of  heat 
required  to  raise  the  temperature  of  unit  weight  of  a  gas  by  one 
degree,  when  the  gas  is  compelled  to  retain  its  original  volume. 

The  former  of  these  exceeds  the  latter  by  the  amount  of  heat  con- 
sumed in  producing  the  expansion. 

A  similar  distinction  exists  in  the  case  of  liquids  and  solids,  but  it 
is  not  often  attended  to.  What  is  always  understood  by  specific  heat 
in  the  case  of  these  bodies  is  in  fact  their  specific  heat  at  constant 
pressure.  The  resistance  of  solids  and  liquids  to  compression  is  so 
enormous  that  a  pressure  of  one  or  two  atmospheres  may  be  neglected 
as  regards  its  effect  upon  their  temperature  and  thermal  capacity. 
But,  in  dealing  with  gases,  the  case  is  far  otherwise,  and  one  of  the 
most  important  data  for  the  solution  of  questions  in  gaseous  mechanics 
is  the  ratio  of  their  two  specific  heats. 

The  best  experiments  on  the  specific  neats  of  gases  are  those  of 
Regnault.  They  have  established  the  two  following  conclusions  for 
specific  heat  at  constant  pressure : — 

(1 )  The  specific  heat  (or  thermal  capacity  per  unit  mass)  of  one  and 
the  same  gas,  whether  simple  or  compound,  is  the  same  at  all  pres- 
sures and  temperatures. 

(2)  The  specific  heats  of  different  simple  gases  are  approximately  in 
the  inverse  ratio  of  their  relative  densities  (§  220),  or  of  their  atomic 


436  CALORIMETRY. 

weights,  according  to  Dulong  and  Pet-it's  law.  This  may  be  other- 
wise expressed  by  saying  that  all  simple  gases  have  nearly  the  same 
thermal  capacity  per  unit  volume,  when  at  the  same  pressure  and 
temperature. 

The  specific  heat  of  dry  air  (at  constant  pressure),  according  to 
Regnault,  is  '2375 ;  that  is  to  say,  the  thermal  capacity  of  a  given 
weight  of  air  is  '2375  of  that  of  an  equal  weight  of  water. 

The  above  conclusions  (I)  and  (2)  are  also  true  of  specific  heat  at 
constant  volume,  as  far  as  regards  simple  gases  and  air  (which,  being 
merely  a  mechanical  mixture,  obeys  the  same  laws  as  a  simple 
gas).  The  two  following  consequences  have  been  experimentally 
confirmed. 

(3)  The  difference  between  the  two  thermal  capacities  per  unit 
volume,  at  a  given  pressure  and  temperature,  is  the  same  for  all 
permanent  gases. 

(4)  The  ratio  of  the  two  specific  heats  is  constant  for  all  simple 
gases,  its  value  being  about  1'4 1. 

It  is  important  to  remark,  that  the  temperatures  of  the  gases  in 
Regnault's  experiments  were  given  by  an  air-thermometer,  so  that 
his  result  as  regards  the  constancy  of  specific  heat  at  all  temperatures 
may  be  thus  stated: — If  equal  quantities  of  heat  be  successively 
added  to  a  gas  at  constant  pressure,  the  volume  of  the  gas  will 
increase  in  arithmetical  progression. 

347  A.  Relation  of  Pressure  to  Volume  when  no  Heat  enters  or 
escapes. — Boyle's  law  asserts  that  the  density  of  a  gas  varies  directly 
as  the  pressure,  when  the  temperature  is  the  same  in  the  cases  com- 
pared. If  no  heat  is  allowed  to  enter  or  escape,  the  temperature  of 
the  gas  will  rise  when  the  pressure  is  increased,  and  the  volume  will 
not  be  so  much  diminished  as  it  would  be  if  the  temperature  remained 
constant. 

Suppose  that  a  quantity  of  gas  at  volume  V,  pressure  P,  and  tem- 
perature T,  receives  a  small  addition  of  heat  q,  the  gas  being  allowed 
to  expand  at  constant  pressure,  so  that  its  volume  becomes  V  +  V,  and 
its  temperature  T  +  t,  its  pressure  being  still  P. 

Now  let  the  gas  be  compressed  without  allowing  any  heat  to  enter 
or  escape,  till  its  volume  is  Y  as  at  first ;  and  let  its  temperature  now 
be  T  +  £  +&,  and  its  pressure  P-j-p. 

It  is  now  sensibly  in  the  same  condition  as  if  the  quantity  q  of 
heat  had  been  imparted  to  it  without  allowing  any  change  of  volume 
to  take  place;  so  that  the  same  quantity  q  of  heat  which  produces  an 


HEAT  OF  FUSION.  437 

elevation  of  temperature  t  at  constant  pressure,  would  produce  an 
elevation  t  +  j3t  at  constant  volume.  The  specific  heats  are  inversely 
as  these  elevations  of  temperature  ;  hence  we  have 

Specific  heat  at  constant  pressure  _  i  ,  o  /o\ 

Specific  heat  at  constant  volume 

To  determine  the  change  of  pressure,  we  have 

V  +  v     1  +  q  (T  +  <  +  j8S).        ,  V  +  tt_l  +  a  (T  +  Q 


.        , 


1  +  a  (T  +  t)  V  1  +  aT     ' 

hence 


_  ..      a  . 

~' 


P  1+aT  1+aT 

therefore  |j=—^^-j  but  we  have  ^  =  ^- 
therefore 


a  result  which  is  of  great  importance  in  connection  with  the  velocity 
of  sound.  In  fact,  experiments  on  the  velocity  of  sound  have  fur- 
nished the  most  precise  determinations  hitherto  made  of  the  value  of 
1  +/3,  which,  as  above  indicated,  is  the  ratio  of  specific  heat  at 
constant  pressure  to  specific  heat  at  constant  volume,  and  is  about 
1-41.1 

348.  Heat  of  Fusion.  —  The  method  of  mixtures  may  be  employed 
to  determine  the  quantity  of  heat  absorbed  by  a  body  in  its  passage 
from  the  solid  to  the  liquid  state.  For  instance,  a  piece  of  ice  at 
zero  is  carefully  weighed  and  plunged  into  water  contained  in  a 
calorimeter.  The  temperature  of  the  water  falls  until  a  certain  limit 
is  attained,  which  is  then  observed.  Suppose  now  that  we  have  the 
following  data:  — 

m  the  thermal  capacity  of  the  calorimeter,  or  the  equivalent  of 
the  calorimeter  in  weight  of  water;  t  its  initial  temperature;  0  its 
final  temperature;  w  the  weight  of  the  ice;  x  the  latent  heat  of 
fusion. 

The  heat  required  to  melt  the  ice  is  wx,  and  the  heat  required  to 

1  It  is  easily  shown,  by  integrating  equation  (3),  that  the  general  relation  between  . 
volume  and  pressure,  when  no  heat  enters  or  escapes,  is 


Vlt  ~V2  denoting  the  volumes  at  pressures  Plf  Pa. 


438  CALORIMETRY. 

raise  the  water  which  it  yields  to  the  temperature  0  is  w  d.  The  sum 
of  these  two  quantities  must  be  equal  to  m  (£  — 0),  the  heat  given  up 
by  the  calorimeter;  that  is, 

w(x  +  0)=m  (t-0), 

from  which  equation  x  is  easily  found.  Since  this  experiment  neces- 
sarily occupies  a  considerable  time,  the  radiation  from  the  calorimeter 
must  be  taken  into  account.  For  this  purpose  a  continual  series  of 
observations  is  taken  of  the  temperatures  indicated  by  the  thermo- 
meter immersed  in  the  liquid,  and  the  quantities  of  heat  gained  or 
lost  are  estimated  by  the  method  described  above  (§  343).  In  this 
way  the  heat  of  fusion  of  ice  was  fixed  by  Laprovostaye  and 
Desains  at  79!25  Centigrade,  which  is  equivalent  to  142  65  Fah- 
renheit. 

When  the  body  melts  at  a  high  temperature,  the  method  is  reversed; 
the  body  is  first  melted,  and  then  immersed  in  the  calorimeter.  In 
doing  this,  precautions  must  be  taken  to  prevent  the  vaporization  of 
a  portion  of  the  water;  for  instance,  the  body  may  be  inclosed  in  a 
small  thin  box  which  is  not  completely  opened  until  towards  the 
close  of  the  experiment.  Suppose  we  have  W,  the  equivalent  of  the 
calorimeter  in  water;  t  its  initial  temperature;  0  its  final  temperature; 
w  the  weight  of  the  body ;  T  its  initial  temperature ;  T'  its  melting- 
point;  c  its  specific  heat  in  the  solid  state;  c  its  specific  heat  in  the 
liquid  state ;  from  these  data  the  equation  will  evidently  be 

W  (e-t)=wx  +  wcT  (T-T')+ivc  (T'-0), 

neglecting  the  correction  for  radiation,  which  can  be  determined  by 
the  ordinary  methods. 

One  of  the  quantities  which  enter  into  this  equation  is  the  specific 
heat  of  the  body  in  the  solid  state,  which  may  be  considered  as  known. 
The  specific  heat  of  the  body  in  the  liquid  state  may  be  deduced  by 
combining  this  equation  with  another  of  the  same  kind,  in  which  the 
initial  temperature  of  the  melted  body  is  different.  In  the  case  oL 
bodies  which,  like  mercury  and  bromine,  are  liquid  at  ordinary  tem- 
peratures, the  specific  heat  in  the  solid  state  can  be  found  by  a  similar 
but  inverse  process. 

The  following  table  gives  the  heats  of  fusion  of  several  substances, 
together  with  their  specific  heats  in  both  states. 


HEAT   OF   EVAPORATION. 


439 


Substances. 

Melting  point. 

Specific 
In  the 

Heats 
In  the 

Latent  Heat  of 
Fusion. 

Solid  State. 

Liquid  State. 

Water,    .     . 

0° 

•5040 

1-0000 

79-250 

Phosphorus, 

44-20 

•2000 

•2000 

5-400 

Sulphur, 

111 

•2020 

•2340 

9-368 

Bromine,     . 

-7'32 

•0840 

•1670 

16-185 

Tin,   .     .     . 

232 

•0560 

•0640 

14-252 

Bismuth,     . 

266 

•0308 

•0363 

12-640 

Lead,      .     . 

326 

•0314 

•0402 

5-369 

Mercury,     . 

-39 

•0319 

•0333 

2-820 

349.  Heat  of  Evaporation. — The  latent  heat  of  evaporation  of 
water,  and  of  some  other  liquids,  can  be  determined  by  means  of 
Despretz's  apparatus,  which  is  shown  in  Fig.  306. 

The  liquid  is  boiled  in  a  retort  C,  which  is  connected  with  a  worm  S 


Fig.  306. — Despretz's  Apparatus. 

surrounded  by  cold  water,  and  terminating  in  the  reservoir  R.  The 
vapour  is  condensed  in  the  worm,  and  collects  in  the  reservoir,  whence 
it  can  be  drawn  by  means  of  the  stop-cock  r.  The  tube  T,  which  is 
fitted  with  a  stop-cock  T',  serves  to  establish  communication  between 
the  reservoir  and  the  atmosphere,  or  between  the  reservoir  and  a 
space  where  a  fixed  pressure  is  maintained,  so  as  to  produce  ebulli- 
tion at  any  temperature  required,  which  is  indicated  by  the  thermo- 


440  CALORIMETRY. 

meter  t     A  is  an  agitator  for  keeping  the  water  at  a  uniform  tem- 
perature, which  is  indicated  by  the  thermometer  t'. 

In  using  the  apparatus,  the  first  step  is  to  boil  the  liquid  in  the 
retort,  and  when  it  is  in  active  ebullition,  it  is  put  in  communication 
with  the  worm.  The  temperature  of  the  calorimeter  has  previously 
been  lowered  a  certain  number  of  degrees  below  that  of  the  surround- 
ing air,  and  the  experiment  ceases  when  it  has  risen  to  the  same 
number  of  degrees  above.  The  compensation  may  thus  be  considered 
as  complete,  since  the  rate  of  heating  is  nearly  uniform. 

If  W  be  the  equivalent  of  the  calorimeter  in  water,  t  its  initial 
temperature,  6  its  final  temperature;  then  the  quantity  of  heat  gained 
by  it  is  W  (0  —  f).  This  heat  comes  partly  from  the  latent  heat  dis- 
engaged at  the  moment  of  condensation  of  the  vapour,  partly  from 
the  loss  of  temperature  of  the  condensed  water,  which  sinks  from  T, 
the  boiling-point  of  the  liquid,  to  the  temperature  of  the  calorimeter. 
If,  then,  x  denote  the  latent  heat  of  evaporation,  w  the  weight  of  the 
liquid  collected  in  the  box  R,  and  c  its  specific  heat,  we  have  the 
equation 

W  (8-t)  =  wx  +  wc  (T-0). 


This  experiment  is  exposed  to  some  serious  causes  of  error.  The 
calorimeter  may  be  heated  by  radiation  from  the  screen  F  which 
protects  it  from  the  direct  radiation  of  the  furnace.  Heat  may  also 
be  propagated  by  means  of  the  neck  of  the  retort.  Again,  the  vapour 
is  not  dry  when  it  passes  into  the  worm,  but  carries  with  it  small 
drops  of  liquid.  Finally,  some  of  the  vapour  may  be  condensed  at 
the  top  of  the  retort,  and  so  pass  into  the  worm  in  a  liquid  state. 
This  last  objection  is  partly  removed  by  sloping  the  neck  of  the 
retort  upwards  from  the  fire,  but  it  sometimes  happens  that  this 
precaution  is  not  sufficient. 

350.  Regnault's  Experiments.  —  The  labours  of  Regnault  in  con- 
nection with  the  subject  of  latent  heat  are  of  the  greatest  importance, 
and  have  resulted  in  the  elaboration  of  a  method  in  which  all  these 
sources  of  error  are  entirely  removed.  The  results  obtained  \)y  him 
are  the  following:  — 

The  quantity  of  heat  required  to  convert  a  kilogramme  of  water 
at  100°  into  vapour,  without  change  of  temperature,  is  537  kilogramme- 
degrees  or  calories. 

If  the  water  were  originally  at  zero,  the  total  amount  of  heat 
required  to  convert  it  into  vapour  at  100°  would  be  637  calories  — 


REGNAULT  S   EXPERIMENTS. 


441 


100  to  raise  it  to  100°,  and  537  more  to  convert  it  into  vapour.  It 
is  this  total  amount  which  is  most  important  to  know  in  the  applica- 
tions of  heat  in  the  arts. 

In  general,  if  Q  denote  the  total  quantity  of  heat1  required  to 
transform  water  at  zero  into  vapour  at  the  temperature  T,  the  value 
of  Q  may  be  deduced  with  great  exactness  from  the  following  equa- 

tion :  — 

Q  =  606-5  +  -305  T.  (a) 

From  what  we  have  said  above,  it  will  be  seen  that  if  A.  denote  the 
latent  heat  of  evaporation  at  temperature  T,  we  must  have 


(6) 


whence,  by  substituting  for  Q  in  (a),  we  have 

X  =  606-5-'695T. 


From  (a)  we  can  find  the  total  heat  for  any  given  temperature,  and 
from  (6)  the  latent  heat  of  evaporation  at  any  given  temperature. 
The  results  for  every  tenth  degree  between  0°  and  230°  are  given  in 
the  following  table:  — 


Temperatures 
Centigrade. 

Latent 
Heat. 

Total 
Heat. 

Temperatures 
Centigrade. 

Latent 
,  Heat. 

Total 
Heat. 

0° 

606 

606 

120°       . 

522 

642 

10 

600 

610 

130 

515 

645 

20 

593 

613 

140 

508 

648 

30 

586 

616 

150 

501 

651 

40 

579 

619 

160 

494 

654 

50 

572 

622 

170       . 

486 

656 

60 

565 

625 

180 

479 

659 

70 

558 

628 

190       . 

472 

662 

80 

551 

631 

200 

464 

664 

90 

544 

634 

210       . 

457 

667 

100 

537 

637 

220 

449 

669 

110 

529 

639 

230       . 

442 

672 

To  reduce  latent  heat  and  total  heat  from  the  Centigrade  to  the 
Fahrenheit  scale,  we  must  multiply  by  -.  Thus  the  latent  and  total 

heat  of  steam  at  212°  F.  are  966'6  and  1146'6.  We  subjoin  a  table, 
taken  from  the  researches  of  Favre  and  Silbermann,  giving  the  latent 
heat  of  evaporation  of  a  number  of  liquids  at  the  temperature  of  their 
boiling-point,  referred  to  the  Centigrade  scale : — 


1  Called  by  Regnault  the  total  heat  of  saturated  vapour  at  T°,  or  the  total  heat  of  vapor- 
ization at  T°. 


442 


CALORIMETRY. 


Boiling- 
point. 

Latent 
Heat. 

Boiling- 
point. 

Latent    ! 
Heat. 

Wood-  spirit, 
Absolute  alcohol,  .     . 
Valeric  alcohol,      .     . 
Ether,     

66-5 

78 
78 
38 

264 
208 
121 
91 

Acetic  acid, 
Butyric  acid, 
Valeric  acid,     . 

120° 
164 
175 
74 

102 
115 
104 
100 

Ethal,     

38 

58 

Oil  of  turpentine, 

156 

69 

Valeric  ether,  . 
Formic  acid,     .     .     . 

113-5 
100 

113-5 
169 

Essence  of  citron, 

165 

70 

'   351.   Heat  Disengaged  in   Chemical  Combinations. — A  very  con- 
venient apparatus  has  been  invented  by  Favre  and  Silbermann  for 


M 


Fig.  307. — Calorimeter  of  Favre  and  Silbermann. 

measuring  the  beat  given  off  in  cbemical  reactions.1  It  is  a  kind  of 
large  mercurial  thermometer  (Fig.  307),  the  reservoir  R  of  which  is 
made  of  iron,  and  contains  one  or  more  cylindrical  openings  similar 
to  that  shown  at  m.  Into  these  are  fitted  tubes  of  glass  or  platinum, 
in  which  the  chemical  reaction  takes  place.  One  of  the  substances 
is  introduced  first,  arid  the  other,  which  is  liquid,  is  then  added  by 
means  of  a  pipette  bent  at  B,  and  containing  the  liquid  in  a  globe, 
as  shown  in  the  figure.  This  is  effected  by  raising  the  pipette  into 
the  position  indicated  by  the  dotted  lines  in  the  figure. 

In  the  upper  part  of  the  reservoir  is  an  opening  fitted  with  a  tube 


1  Chemical  actions  are  called  reactions,  and  a  substance  which  acts  chemically  is  called 
a  reagent.     The  names  are  awkward,  but  are  in  general  use. 


HEAT   OF   COMBUSTION. 


443 


containing  a  steel  plunger  P,  which  descends  into  the  mass  of  mer- 
cury, and  can  be  screwed  down  or  up  by  turning  the  handle  M.  To 
prepare  the  apparatus  for  use,  the  plunger  is  so  adjusted  that  the 
mercury  stands  at  the  zero-point  of  the  graduated  tube  tt',  the  reac- 
tion is  then  allowed  to  take  place,  and  the  movement  of  the  mer- 
curial column  is  observed  with  the  telescope  L.  In  order  to  measure 
the  quantity  of  heat  corresponding  to  this  displacement,  a  known 
weight  of  hot  water  is  introduced  into  the  reservoir,  and  allowed  to 
give  up  its  heat  to  the  mercury ;  the  displacement  of  the  mercurial 
column  is  then  observed,  and  since  the  quantity  of  heat  correspond- 
ing to  this  displacement  is  known,  that  corresponding  to  any  other 
displacement  can  easily  be  calculated.  The  iron  reservoir  is  inclosed 
in  a  box  filled  with  wadding  or  some  other  non-conducting  material.1 

When  the  chemical  reaction  takes  the 
form  of  combustion,  a  different  arrange- 
ment is  necessary.  An  apparatus  of  great 
perfection  has  been  devised  by  Favre  and 
Silbennann  for  this  purpose,  but  it  is  of 
too  complex  a  construction  to  be  de- 
scribed here.  A  sufficiently  accurate  idea 
of  the  general  method  adopted  in  these 
cases  will  be  obtained  by  a  study  of  the 
much  simpler  apparatus  employed  for 
the  same  purpose  by  Dulong. 

It  consists  of  a  combustion-chamber  C 
surrounded  by  the  water  contained  in  a 
calorimeter  D,  in  which  moves  an  agitator 
whose  stem  is  shown  at  A.  The  com- 
bustible substance,  if  it  be  a  gas,  is  con- 
ducted into  the  chamber  through  the 
tube  h,  and  the  oxygen  necessary  for 

its  combustion  enters  by  one  of  the  tubes  /  or  p.  The  products 
of  combustion  pass  through  the  worm  8,  and  finally  escape,  but 

1  In  the  mode  of  experimentation  adopted  by  Dr.  Andrews,  the  combination  takes  place 
in  a  thin  copper  vessel  inclosed  in  a  calorimeter  of  water  to  which  it  gives  up  its  heat;  and 
the  rise  of  temperature  in  the  water  is  observed  with  a  very  delicate  thermometer,  the 
water  being  agitated  either  by  stirring  with  a  glass  rod  or  by  making  the  whole  apparatus 
revolve  about  a  horizontal  axis. 

In  experimenting  on  the  heat  of  combustion,  the  oxygen  and  the  substance  to  be  burned 
are  introduced  into  the  thin  copper  vessel,  which  is  inclosed  in  the  calorimeter  as  above, 
and  ignition  or  explosion  is  produced  by  means  of  electricity. 


Fig.  308. — Dulong's  Calorimeter  for 
Combustion. 


444 


CALORIMETRY. 


not  until  they  have  fallen  to  the  temperature  of  the  water  in  the 
calorimeter.  This  condition  is  necessary  to  the  exactness  of  the 
result,  and  its  precise  fulfilment  is  verified  by  observing  the  tem- 
peratures indicated  by  the  thermometers  t  and  tf,  the  former  of  which 
gives  the  temperature  of  the  water,  and  the  latter  that  of  the  pro- 
ducts of  combustion  at  their  exit.  These  two  temperatures  should 
always  agree.  The  progress  of  the  combustion  is  observed  through 
the  opening  p,  which  is  closed  by  a  piece  of  glass.  Some  of  the 
results  obtained  by  this  method  are  given  in  the  following  table,  the 
combustion  being  supposed  to  take  place  in  oxygen,  with  the  excep- 
tion of  the  second  example  on  the  list 

HEATS  OF  COMBUSTION. l 
(Referred  to  the  Centigrade  Scale.) 


Hydrogen, 34,462 

Hydrogen  with  chlorine,     .  23,783 

Carbonic  oxide,     ....  3,403 

Marsh-gas, 13,063 

Charcoal, 8,080 

Graphite, 7,797 

Diamond, 7,770 

Native  sulphur,    ....  2,261 


Soft  sulphur, 2,258 

Sulphide  of  carbon,     .     .     .  3,400 

Olefiantgas, 11,857 

Ether, 9,028 

Alcohol, 7,184 

Stearic  acid, 9,616 

Oil  of  turpentine,    .     .     .     .10,852 

Olive-oil, 9,862 


Of  all  substances  hydrogen  possesses  by  far  the  greatest  heat  of 
combustion.  This  fact  accounts  for  the  intense  heating  effects  which 
can  be  obtained  with  the  oxy-hydrogen  blowpipe,  in  which  an  annular 
jet  of  hydrogen  is  completely  burned  by  means  of  a  central  jet  of  oxygen. 
It  is  to  be  observed  that  the  heat  of  combination  observed  by  the 
above  methods  includes  the  heating  or  cooling  effect  of  the  changes 
of  volume  which  usually  accompany  chemical  combination. 

1  These  numbers  denote  the  number  of  times  its  own  weight  of  water  which  would  be 
raised  one  degree  Centigrade  by  the  heat  evolved  in  the  combustion  of  the  substance.  For 
example,  the  combustion  of  a  pound  of  charcoal  gives  out  enough  heat  to  raise,  8080  pounds 
of  water  one  degree. 


CHAPTEE   XXXIL 


THERMODYNAMICS. 

354.  Connection  between  Heat  and  Work. — That  heat  can  be  made 
to  produce  work  is  evident  when  we  consider  that  the  work 

done  by  steam-engines  and  other  heat-engines  is  due  to  this 
source. 

Conversely,  by  means  of  work  we  can  produce  heat.  Fig. 
310  represents  an  apparatus  sometimes  called  the  pneumatic 
tinder-box,  consisting  of  a  piston  working  tightly  in  a  glass 
barrel.  If  a  piece  of  gun-cotton  be  fixed  in  the  cavity  of 
the  piston,  and  the  air  be  then  suddenly  compressed,  so  much 
heat  will  be  developed  as  to  inflame  the  gun-cotton. 

A  singular  explanation  of  this  effect  was  at  one  time  put 
forward.  It  was  maintained  that  heat  or  caloric  was  a  kind 
of  imponderable  fluid,  which,  when  introduced  into  a  body, 
produced  at  once  an  increase  of  volume  and  an  elevation 
of  temperature.  If,  then,  the  body  was  compressed,  the 
caloric  which  had  served  to  dilate  it  was,  so  to  speak, 
squeezed  out,1  and  hence  the  development  of  heat.  An 
immediate  consequence  of  this  theory  is  that  heat  cannot  be. 
increased  or  diminished  in  quantity,  but  that  any  addition 
to  the  quantity  of  heat  in  one  part  of  a  system  must  be 
compensated  by  a  corresponding  loss  in  another  part.  But 
we  know  that  there  are  cases  in  which  heat  is  produced  by 
two  bodies  in  contact,  without  our  being  able  to  observe  any 
traces  of  this  compensating  process.  An  instance  of  this  is 
the  production  of  heat  by  friction. 

355.  Heat  produced  by  Friction. — Friction  is  a  well-known      Fig  310 

Pneumatic 

1  In  other  words,  the  thermal  capacity  of  the  body  was  supposed  to  be 
diminished,  so  that  the  amount  of  heat  contained  in  it,  without  undergoing  any  increase, 
was  able  to  raise  it  to  a  higher  temperature. 


446  THERMO-DYNAMICS. 

source  of  heafc.  Savages  are  said  to  obtain  fire  by  rubbing  two  pieces 
of  dry  wood  together.  The  friction  between  the  wheel  and  axle  in 
railway-carriages  frequently  produces  the  same  effect,  when  they 
have  been  insufficiently  greased;  and  the  stoppage  of  a  train  by 
applying  a  brake  to  the  wheels  usually  produces  a  shower  of  sparks. 
The  production  of  heat  by  friction  may  be  readily  exemplified  by 
the  following  experiment,  due  to  Tyndall.  A  glass  tube  containing 
water  (Fig.  311),  and  closed  by  a  cork,  can  be  rotated  rapidly  about 


Fig.  311.— Heat  produced  by  Friction. 

its  axis.  While  thus  rotating,  it  is  pressed  by  two  pieces  of  wood, 
covered  with  leather.  The  water  is  gradually  warmed,  and  finally 
enters  into  ebullition,  when  the  cork  is  driven  out,  followed  by  a  jet 
of  steam.  Friction,  then,  may  produce  an  intense  heating  of  the 
bodies  rubbed  together,  without  any  corresponding  loss  of  heat  else- 
where. 

At  the  close  of  last  century,  Count  Rum  ford  (an  American  in  the 
service  of  the  Bavarian  government)  called  attention  to  the  enormous 
amount  of  heat  generated  in  the  boring  of  cannon,  and  found,  in  a 
special  experiment,  that  a  cylinder  of  gun-metal  was  raised  from  the 
temperature  of  60°  F.  to  that  of  130°  F.  by  the  friction  of  a  blunt  steel 

borer,  during  the  abrasion  of  a  weight  of  metal  equal  to  about  ^  of 
the  whole  mass  of  the  cylinder.  In  another  experiment,  he  sur- 
rounded the  gun  by  water  (which  was  prevented  from  entering  the 
bore),  and,  by  continuing  the  operation  of  boring  for  2|-  hours,  he 


TY  OF  CALIFORNIA 

447 


made  this  water  boil.  In  reasoning  from  these  experiments,  he 
strenuously  maintained  that  heat  cannot  be  a  material  substance,  but 
must  consist  in  motion. 

The  advocates  of  the  caloric  theory  endeavoured  to  account  for 
these  effects  by  asserting  that  caloric,  which  was  latent  in  the  metal 
when  united  in  one  solid  mass,  had  been  forced  out  and  rendered 
sensible  by  the  process  of  disintegration  under  heavy  pressure.  This 
supposition  was  entirely  gratuitous,  no  difference  having  ever  been 
detected  between  the  properties  of  entire  and  of  comminuted  metal 
as  regards  thermal  capacity  ;  and,  to  account  for  the  observed  effect, 
the  latent  heat  thus  supposed  to  be  rendered  sensible  in  the  abrasion 
of  a  given  weight  of  metal,  must  be  sufficient  to  raise  950  X  70,  that  is 
66,500  times  its  own  weight  of  metal  through  1°. 

Yet,  strange  to  say,  the  caloric  theory  survived  this  exposure  of 
its  weakness,  and  the,  if  possible,  still  more  conclusive  experiment 
of  Sir  Humphrey  Davy,  who  showed  that  two  pieces  of  ice,  when 
rubbed  together,  were  converted  into  water,  a  change  which  involves 
not  the  evolution  but  the  absorption  of  latent  heat,  and  which  cannot 
be  explained  by  diminution  of  thermal  capacity,  since  the  specific 
heat  of  water  is  much  greater  than  that  of  ice. 

Davy,  like  Rumford,  maintained  that  heat  consisted  in  motion, 
and  the  same  view  was  maintained  by  Dr.  Thos.  Young  ;  but  the 
doctrine  of  caloric  nevertheless  continued  to  be  generally  adopted 
until  about  the  year  1840,  since  which  time,  the  experiments  of  Joule, 
the  eloquent  advocacy  of  Meyer,  and  the  mathematical  deductions  of 
Thomson,  Rankine,  and  Clausius,  have  completely  established  the 
mechanical  theory  of  heat,  and  built  up  an  accurate  science  of  thermo- 
dynamics. 

356.  Foucault's  Experiment.  —  The  relations  existing  between  elec- 
trical and  thermal  phenomena  had  considerable  influence  in  leading 
to  correct  views  regarding  the  nature  of  heat.  An  experiment 
devised  by  Foucault  illustrates  these  relations,  and  at  the  same 
time  furnishes  a  fresh  example  of  the  production  of  heat  by  the 
performance  of  mechanical  work. 

The  apparatus  consists  (Fig.  312)  of  a  copper  disc  which  can  be 
made  to  rotate  with  great  rapidity  by  means  of  a  system  of  toothed 
wheels.  The  motion  is  so  free  that  a  very  slight  force  is  sufficient  to 
maintain  it.  The  disc  rotates  between  two  pieces  of  iron,  constituting 
the  armatures  of  one  of  those  temporary  magnets  which  are  obtained 
by  the  passage  of  an  electric  current  (called  electro-magnets).  If, 


448 


THERMO-DYNAMICS. 


while  the  disc  is  turning,  the  current  is  made  to  pass,  the  armatures 
become  strongly  magnetized,  and  a  peculiar  action  takes  place  between 
them  and  the  disc,  consisting  in  the  formation  of  induced  currents  in 
the  latter,  accompanied  by  a  resistance  to  motion.  As  long  as  the 


Fig.  312.— Foucault's  Apparatus. 

magnetization  is  continued,  a  considerable  effort  is  necessary  to 
maintain  the  rotation  of  the  disc ;  and  if  the  rotation  be  continued 
for  two  or  three  minutes,  the  disc  will  be  found  to  have  risen  some 
50°  or  60°  C.  in  temperature,  the  heat  thus  acquired  by  the  disc  being 
the  equivalent  of  the  work  done  in  maintaining  the  motion.  It  is 
to  be  understood  that,  in  this  experiment,  the  rotating  disc  does  not 
touch  the  armatures ;  the  resistance  which  it  experiences  is  due  en- 
tirely to  invisible  agencies. 

The  experiment  may  be  varied  by  setting  the  disc  in  very  rapid 


MECHANICAL   EQUIVALENT   OF   HEAT. 


449 


rotation,  while  no  current  is  passing,  then  leaving  it  to  itself,  and 
immediately  afterwards  causing  the  current  to  pass.  The  result  will 
be,  that  the  disc  will  be  brought  to  rest  almost  instantaneously,  and 
will  undergo  a  very  slight  elevation  of  temperature,  the  heat  gained 
being  the  equivalent  of  the  motion  which  is  destroyed. 

357.  Mechanical  Equivalent  of  Heat. — The  most  precise  determina- 
tion yet  made  of  the  numerical  relation  subsisting  between  heat  and 
mechanical  work  was  obtained  by  the  following  experiment  of  Joule. 
He  constructed  an  agitator  which  is  somewhat  imperfectly  repre- 
sented in  Fig.  313,  consisting  of  a  vertical  shaft  carrying  several  sets 
of  paddles  revolving  between  stationary  vanes,  these  latter  serving 


Fig.  313.— Determination  of  the  Mechanical  Equivalent  of  Heat 

to  prevent  the  liquid  in  the  vessel  from  being  bodily  whirled  in  the 
direction  of  rotation.  The  vessel  was  filled  with  water,  and  the 
agitator  was  made  to  revolve  by  means  of  a  cord,  wound  round  the 
upper  part  'of  the  shaft,  carried  over  a  pulley,  and  attached  to  a 
weight,  which  by  its  descent  drove  the  agitator,  and  furnished  a 
measure  of  the  work  done.  The  pulley  was  mounted  on  friction- 
wheels,  and  the  weight  could  be  wound  up  without  moving  the 
paddles.  When  all  corrections  had  been  applied,  it  was  found  that 
the  heat  communicated  to  the  water  by  the  agitation  amounted  to 
one  pound-degree  Fahrenheit  for  every  772  foot-pounds  of  work 
spent  in  producing  it.  This  result  was  verified  by  various  other 
forms  of  experiment,  and  may  be  assumed  to  be  correct  within  about 
one  foot-pound.  The  experiments  were  made  at  Manchester,  where 

29 


450  THERMODYNAMICS. 

<7  is  32  194,  and  it  is  to  be  borne  in  mind  that  a  foot-pound  does  not 
denote  precisely  the  same  amount  of  work  at  all  places  on  the  earth's 
surface,  but  varies  in  direct  proportion  to  the  intensity  of  gravity. 
The  difference  in  its  value  in  passing  from  one  place  to  another  on 
the  earth  is,  however,  not  greater  than  the  probable  error  of  the 
number  772.  We  may  therefore,  with  about  as  much  accuracy  as  is 
warranted  by  the  present  state  of  our  knowledge,  assert  that  the 
energy  comprised  in  one  pound-degree  Fahrenheit  is  about  772  terres- 
trial foot-pounds.1 

The  mechanical  equivalent  of  the  pound-degree  Centigrade  is  -g  of 

this,  or  about  1390  foot-pounds. 

The  number  772  or  1390,  according  to  the  scale  of  temperature 
adopted,  is  commonly  called  Joules  equivalent,  and  is  denoted  in 
formulas  by  the  letter  J.  If  we  take  the  kilogramme-degree  Cent!' 
grade  for  unit  of  heat,  and  the  kilogrammetre  for  unit  of  work,  the 
value  of  J  will  be  424. 

357  A.  First  Law  of  Thermo-dynamics.  —  Whenever  work  is  per- 
formed by  the  agency  of  heat,  an  amount  of  heat  disappears  equi- 
valent to  the  work  performed  ;  and  whenever  mechanical  work  is 
spent  in  generating  heat,  the  heat  generated  is  equivalent  to  the 
work  thus  spent;  that  is  to  say,  we  have  in  both  cases 


W  denoting  the  work,  H  the  heat,  and  J  Joule's  equivalent.  This 
is  called  the  first  law  of  thermo-dynamics,  and  it  is  a  particular  case 
of  the  great  natural  law  (§  53  K)  which  asserts  that  energy  may  be 
transmuted,  but  is  never  created  or  destroyed. 

It  may  be  well  to  remark  here  that  work  is  not  energy,  but  is 
rather  the  process  by  which  energy  is  transmuted  (§  53  J),  amount  of 
work  being  measured  by  the  amount  of  energy  transmuted.  When- 
ever work  is  done,  it  leaves  an  effect  behind  it  in  the  shape  of  energy 
of  some  kind  or  other,  equal  in  amount  to  the  energy  consumed  in 
performing  the  work,  or,  in  other  words,  equal  to  the  work  itself. 

As  regards  the  nature  of  heat,  there  can  be  little  doubt  that  heat 
properly  so  called,  that  is  sensible  as  distinguished  from  latent  heat, 
consists  in  some  kind  of  motion,  and  that  quantity  of  heat  is  quan- 

1  In  absolute  units  of  work,  of  which  a  foot-pound  contains  g,  the  equivalent  of  a  pound- 
degree  Fahrenheit  is  772  x  32-194  =  24854,  which  is  within  less  than  1  per  cent,  of  25,000. 
Hence  the  heat-  equivalent  of  the  kinetic  energy  of  a  mass  of  m  pounds  moving  with  a  velo- 
city of  v  feet  per  second  is  approximately  4  wv2  -r-  25000,  or  2  m?>2  -i-  100000. 


FIRST  LA.W  OF  THERMODYNAMICS.  451 

tity  of  energy  of  motion,  or  kinetic  energy  (§  53 1),  whereas  latent 
heat  consists  in  energy  of  position  or  potential  energy  (§  53  j). 

We  have  already  had,  in  the  experiments  of  Rumford,  Davy, 
Foucault,  and  Joule,  some  examples  of  transmutation  of  energy;  but 
it  will  be  instructive  to  consider  some  additional  instances. 

When  a  steam-engine  is  employed  in  hauling  up  coals  from  a  pit, 
an  amount  of  heat  is  destroyed  in  the  engine  equivalent  to  the  energy 
of  position  which  is  gained  by  the  coal. 

In  the  propulsion  of  a  steam-boat  with  uniform  velocity,  or  in  the 
drawing  of  a  railway  train  with  uniform  velocity  on  a  level,  there  is 
no  gain  of  potential  energy,  neither  is  there,  as  far  as  the  vessel  or 
train  is  concerned,  any  gain  of  kinetic  energy.  In  the  case  of  the 
steamer,  the  immediate  effect  consists  chiefly  in  the  agitation  of  the 
water,  which  involves  the  generation  of  kinetic  energy;  and  the 
ultimate  effect  of  this  is  a  warming  of  the  water,  as  in  Joule's  experi- 
ment. In  the  case  of  the  train,  the  work  done  in  maintaining  the 
motion  is  spent  in  friction  and  concussions,  both  of  which  operations 
give  heat  as  the  ultimate  effect.  Here,  then,  we  have  two  instances 
in  which  heat,  after  going  through  various  transformations,  reappears 
as  heat  at  a  lower  temperature. 

In  starting  a  train  on  a  level,  the  heat  destroyed  in  the  engine 
finds  its  equivalent  mainly  in  the  energy  of  motion  gained  by  the 
train ;  and  this  energy  can  again  be  transformed  into  heat  by  turning 
off  the  steam  and  applying  brakes  to  the  wheels. 

When  a  cannon-ball  is  fired  against  an  armour  plate,  it  is  heated 
red-hot  if  it  fails  to  penetrate  the  plate,  the  energy  of  the  moving 
ball  being  in  this  case  obviously  converted  into  heat.  If  the  plate 
is  penetrated,  and  the  ball  lodges  in  the  wooden  backing,  or  in  a 
bank  of  earth,  the  ball  will  not  be  so  much  heated,  although  the  total 
amount  of  heat  generated  must  still  be  equivalent  to  the  energy  of 
motion  destroyed.  The  ruptured  materials,  in  fact,  receive  a  large 
portion  of  the  heat.  The  heat  produced  in  the  rupture  of  iron  is  well 
illustrated  by  punching  and  planing  machines,  the  pieces  of  iron 
punched  out  of  a  plate,  or  the  shavings  planed  off  it,  being  so  hot 
that  the}7  can  scarcely  be  touched,  although  the  movements  of  the 
punch  and  plane  are  exceedingly  slow.  The  heat  gained  by  the  iron 
is,  in  fact,  the  equivalent  of  the  work  performed,  and  this  work  is 
considerable  on  account  of  the  great  force  required. 

357  B.  Heat  Lost  in  Expansion. — The  difference  between  the  specific 
heat  of  a  gas  at  constant  pressure  and  at  constant  volume,  is  almost 


452  THERMO -DYNAMICS. 

exactly  the  equivalent  of  the  work  which  the  gas  at  constant  pres- 
sure performs  in  pushing  back  the  surrounding  atmosphere.  Joule 
immersed  two  equal  vessels  in  water,  one  of  them  containing  highly- 
compressed  air,  and  the  other  being  exhausted ;  and  when  they  were 
both  at  the  temperature  of  the  water  he  opened  a  stop-cock  which 
placed  the  vessels  in  communication.  The  compressed  air  thus 
expanded  to  double  its  volume,  but  the  temperature  of  the  surround- 
ing water  was  unaltered,  the  heat  converted  into  energy  of  motion 
by  the  expansion  being,  in  fact,  compensated  by  the  heat  generated 
in  the  destruction  of  this  motion  in  the  previously  vacuous  vessel. 
This  experiment  shows  that,  when  air  expands  without  having  to 
overcome  external  resistances,  its  temperature  is  not  sensibly  changed 
by  the  expansion. 

Suppose  we  have  a  cylinder  whose  internal  section  is  a  square 
decimetre,  and  that  a  piston  travelling  in  this  cylinder  is  pushed 
outwards  by  the  expansion  of  air  in  the  cylinder.  Let  the  air  be 
initially  at  0°  C.,  and  occupy  1  decimetre  in  length  of  the  cylinder, 
so  that  its  volume  at  this  temperature  is  a  cubic  decimetre,  and  let 
this  air  be  expanded  at  the  constant  pressure  of  760  mm.  by  the 
addition  of  Jieat,  until  it  occupies  double  its  initial  volume,  and  has 
therefore  pushed  the  piston  a  distance  of  1  decimetre.  Since  air 

expands  by  ^3  of  its  volume  at  0°  for  each  degree,  the  final  tempera- 
ture will,  in  this  case,  be  273°  Q,  and  since  the  specific  heat  of  air  at 
constant  pressure  is  -237,  and  the  weight  of  the  air  is  1'293  gramme, 
the  heat  taken  up  by  the  air  is 

273  x  -237  x  1'293  =  S3'66  gramme -degrees. 

Now  the  pressure  of  760  mm.  is  equivalent  to  1-0.33  kilogrammes  per 
square  centimetre;  hence  the  total  pressure  resisting  the  advance  of 
the  piston  is  103 '3  kilogrammes,  which  is  overcome  through  a  dis- 
tance of  1  decimetre,  so  that  the  work  done  against  atmospheric 
resistance  is  10 '33  kilogramme tres. 

Joule's  equivalent  for  a  kilogramme- degree  is  424  kilogrammetres. 
The  heat- equivalent  of  the  work  done  in  the  present  case  is  there- 

-i  s\ .00 

fore  -^  —  '02436  kilogramme-degree  =  24 '36  gramme-degrees. 

Hence,  of  the  whole  heat  83 '66  received  by  the  air  in  the  cylinder, 
24'36  has  been  spent  in  doing  external  work,  leaving  59  3  as  the 
amount  which  would  have  sufficed  to  raise  the  air  to  the  same  tem- 
perature if  no  external  work  had  been  performed.  Now  the  ratio 


THERMIC   ENGINES.  453 

of  83-G6  to  59'3  is  1-41,  which,  as  we  have  already  seen  (§  347),  is 
the  ratio  of  specific  heat  at  constant  pressure  to  specific  heat  at  con- 
stant volume. 

In  the  case  of  air  and  perfect  gases,  the  heat  gained  by  compres- 
sion or  lost  in  expansion  is  almost  the  exact  equivalent  of  the 
external  work  performed. 

In  view  of  these  facts,  the  specific  heat  of  a  gas  at  constant  volume 
is  often  called  the  true  specific  heat  of  the  gas.  The  heat  required 
to  produce  a  given  change  of  temperature  in  a  gas,  when  its  volume 
changes  in  any  specified  way,  may  be  computed  to  a  very  close 
approximation  -by  calculating  the  work  done  by  the  gas  against 
external  resistances  during  its  change  of  volume,  and  adding  the 
heat-equivalent  of  this  work  to  the  heat  which  would  have  produced 
the  same  change  of  temperature  at  constant  volume.  The  true 
specific  heat  of  air  in  this  sense  is  '168. 

358.  Thermic  Engines. — In  every  form  of  thermic  engine,  work  is 
obtained  by  means  of  expansion  produced  by  heat,  the  force  of  ex- 
pansion being  usually  applied  by  admitting  a  hot  elastic  fluid  to 
press  alternately  on  opposite  sides  of  a  piston  travelling  in  a  cylinder. 
Of  the  heat  received  by  the  elastic  fluid  from  the  furnace,  a  part 
leaks  out  by  conduction  through  the  sides  of  the  containing  vessels, 
another  part  is  carried  out  by  the  fluid  when  it  escapes  into  the  air 
or  into  the  condenser,  the  fluid  thus  escaping  being  always  at  a 
temperature  lower  than  that  at  which  it  entered  the  cylinder,  but 
higher  than  that  of  the  air  or  condenser  into  which  it  escapes;  but 
a  third  part  has  disappeared  altogether,  and  ceased  to  exist  as  heat, 
having  been  spent  in  the  performance  of  work.  This  third  part  is 
the  exact  equivalent  of  the  work  performed  by  the  elastic  fluid  in 
driving  the  piston,1  and  may  therefore  be  called  the  heat  utilized,  or 
the  heat  converted. 

The  efficiency  of  an  engine  may  be  measured  by  the  ratio  of  the 
heat  thus  converted  to  the  whole  amount  of  heat  which  enters  the 
engine;  and  we  shall  use  the  word  efficiency  in  this  sense. 

358  A.  Carnot's  Investigations. — The  first  approach  to  an  exact 
science  of  thermo-dynamics  was  made  by  Carnot  in  1824.  By  rea- 
soning based  on  the  theory  which  regards  heat  as  a  substance,  but 
which  can  be  modified  so  as  to  remain  conclusive  when  heat  is 


1  If  negative  work  is  done  by  the  fluid  in  any  part  of  the  stroke  (that  is,  if  the  piston 
presses  back  the  fluid),  the  algebraic  sum  of  work  is  to  be  taken. 


454  THERMODYNAMICS. 

regarded  as  a  form  of  energy,  he  established  the  following  prin- 
ciples:— 

I.  The  thermal  agency  by  which  mechanical  effect  may  be  obtained 
is  the  transference  of  heat  from  one  body  to  another  at  a  lower  tem- 
perature.    These  two  bodies  he  calls  the  source  and  the  refrigerator. 
Adopting  the  view  generally  received  at  that  time  regarding  the 
nature  of  heat,  he  supposed  that  all  the  heat  received  by  an  engine 
was  given  out  by  it  again  as  heat;  so  that,  if  all  lateral  escape  was 
prevented,  all  the  heat  drawn  by  the  engine  from  the  source  was 
given  by  the  engine  to  the  refrigerator,  just  as  the  water  which  by 
its  descent  turns  a  mill-wheel,  runs  off  in  undiminished  quantity  at 
a  lower  level.     We  now  know  that,  when  heat  is  let  down  through 
an  engine  from  a  higher  to  a  lower  temperature,  it  is  diminished  in 
amount  by  the  equivalent  of  the  work  done  by  the  engine  against 
external  resistances. 

He  further  shows  that  the  amount  of  work  which  can  be  obtained 
by  letting  down  a  given  quantity  of  heat — or,  as  we  should  say  with 
our  present  knowledge,  by  partly  letting  it  down  and  partly  con- 
suming it  in  work,  is  increased  by  raising  the  temperature  of  the 
source,  or  by  lowering  the  temperature  of  the  refrigerator;  and  estab- 
lishes the  following  important  principle: — 

II.  A  perfect  thermo-dynamic  engine  is  such  that,  whatever  amount 
of  mechanical  effect  it  can  derive  from  a  certain  thermal  agency; 
if  an  equal  amount  be  spent  in  working  it  backwards,  an  equal 
reverse  thermal  effect  will  be  produced.     This  is  often  expressed  by 
saying  that  a  completely  reversible  engine  is  a  perfect  engine. 

By  a  perfect  engine  is  here  meant  an  engine  which  possesses  the 
maximum  of  efficiency  compatible  with  the  given  temperatures  of  its 
source  and  refrigerator;  and  Carnot  here  asserts  that  all  completely 
reversible  engines  attain  this  maximum  of  efficiency.  The  proof  of 
this  important  principle,  when  adapted  to  the  present  state  of  our 
knowledge,  is  as  follows: — 

Let  there  be  two  thermo-dynamic  engines,  A  and  B,  working 
between  the  same  source  and  refrigerator;  and  let  A  be  completely 
reversible.  Let  the  efficiency  of  A  be  m,  so  that,  of  the  quantity  Q 
of  heat  which  it  draws  from  the  source,  it  converts  m  Q  into  mechan- 
ical effect,  and  gives  Q— 771 Q  to  the  refrigerator,  when  worked  for- 
wards. Accordingly,  when  worked  backwards,  with  the  help  of 
work  mQ  applied  to  it  from  without,  it  takes  Q— wQ  from  the 
refrigerator,  and  gives  Q  to  the  source. 


SECOND   LAW   OF   THERMO-DYNAMICS.  455 

In  like  manner,  let  the  efficiency  of  B  be  mf,  so  that,  of  heat  Q' 
which  it  draws  from  the  source,  it  converts  m'Q,'  into  mechanical 
effect,  and  gives  Q'— m'Q'to  the  refrigerator. 

Let  this  engine  be  worked  forwards,  and  A  backwards.  Then, 
upon  the  whole,  heat  to  the  amount  Q'— Q  is  drawn  from  the  source, 
heat  ra'Q'  —  mQ  is  converted  into  mechanical  effect,  and  heat 
Q'_Q_(m'Q'— mQ)  is  given  to  the  refrigerator. 

If  we  make  m'Q'=mQ,  that  is,  if  we  suppose  the  external  effect 

to  be  nothing,  heat  to  the  amount  Q'— Q  or  (^/-i)  Q  is  carried  from 
the  source  to  the  refrigerator,  if  m  be  greater  than  m',  that  is,  if  the 
reversible  engine  be  the  more  efficient  of  the  two.  If  the  other 

engine  be  the  more  efficient,  heat  to  the  amount  (1~~')  Q  is  trans- 
ferred from  the  refrigerator  to  the  source,  or  heat  pumps  itself  up 
from  a  colder  to  a  warmer  body,  and  that  by  means  of  a  machine 
which  is  self-acting,  for  B  does  work  which  is  just  sufficient  to  drive  A. 
Such  a  result  we  are  entitled  to  assume  impossible,  therefore  B  cannot 
be  more  efficient  than  A. 

Another  proof  is  obtained  by  making  Q'=Q.  The  source  then 
neither  gains  nor  loses  heat,  and  the  refrigerator  gains  (m— m')  Q, 
which  is  derived  from  work  performed  upon  the  combined  engine 
from  without,  if  A  be  more  efficient  than  B.  If  B  were  the  more 
efficient  of  the  two,  the  refrigerator  would  lose  heat  to  the  amount 
(m'— m)  Q,  which  would  yield  its  full  equivalent  of  external  work, 
and  thus  a  machine  would  be  kept  going  and  doing  external  work 
by  means  of  heat  drawn  from  the  coldest  body  in  its  neighbourhood, 
a  result  which  cannot  be  admitted  to  be  possible. 

358s.  Second  Law  of  Thermo-dynamics. — It  follows,  from  the  prin- 
ciple thus  established,  that  all  reversible  engines  with  the  same  tem- 
peratures of  source  and  refrigerator  have  the  same  efficiency,  whether 
the  working  substance  employed  in  them  be  steam,  air,  or  any  other 
material,  gaseous,  liquid,  or  solid.  Hence  we  can  lay  down  the  fol- 
lowing law,  which  is  called  the  second  law  of  thermo-dynamics :  the 
efficiency  of  a  completely  reversible  engine  is  independent  of  the  nature 
of  the  working  substance,  and  depends  only  on  the  temperatures  at 
which  the  engine  takes  in  and  gives  out  heat;  and  the  efficiency  of 
such  an  engine  is  the  limit  of  possible  efficiency  for  any  engine. 

As  appendices  to  this  law  it  has  been  further  established : 

1.  That  when  one  of  the  two  temperatures  is  fixed,  the  efficiency 
is  simply  proportional  to  the  difference  between  the  two,  provided 


456  THERMODYNAMICS. 

this  difference  is  very  small.  This  holds  good  for  all  scales  of  tem- 
perature. 

2.  From  calculations  relating  to  an  imaginary  engine  of  special 
simplicity,  in  which  a  permanent  gas  is  the  working  substance,  it 

has  been  determined  that  the  efficiency  of  a  reversible  engine  is 

T-T' 

approximately  T  ,  T  denoting  the  upper,  and  T'  the  lower  tem- 
perature between  which  the  engine  works,  reckoned  from  absolute 
zero  (§  219  A),  on  the  air-thermometer.  This  is  more  easily  remem- 
bered when  stated  in  the  following  more  symmetrical  form.  Let  Q 
denote  the  quantity  of  heat  taken  in  at  the  absolute  temperature  T, 
Q'  the  quantity  given  out  at  the  absolute  temperature  T',  and  con- 
sequently Q— Q'  the  heat  converted  into  mechanical  effect,  then  we 
shall  have  approximately 

Q  =  Q'  _  Q-Q' 
T       T'        T-T'- 

358 c.  Absolute  Scale  of  Temperature. — In  ordinary  thermometers, 
temperatures  are  measured  by  the  apparent  expansion  of  a  liquid  in 
a  glass  envelope.  If  two  thermometers  are  constructed,  one  with 
mercury  and  the  other  with  alcohol  for  its  liquid,  it  is  obviously 
possible  to  make  their  indications  agree  at  two  fixed  temperatures. 
If,  however,  the  volume  of  the  tube  intervening  between  the  two 
fixed  points  thus  determined  be  divided  into  the  same  number  of 
equal  parts  in  the  two  instruments,  and  the  divisions  be  numbered 
as  degrees  of  temperature,  the  two  instruments  will  give  different 
indications  if  plunged  in  the  same  bath  at  an  intermediate  tempera- 
ture, and  they  will  also  differ  at  temperatures  lying  beyond  the  two 
fixed  points.  It  is  a  simple  matter  to  test  equality  of  temperature, 
but  it  is  far  from  simple  to  decide  upon  a  test  of  equal  differences  of 
temperature.  Different  liquids  expand  not  only  by  different  amounts 
but  by  amounts  which  are  not  proportional,  no  two  liquids  being 
in  this  respect  in  agreement. 

In  the  case  of  permanent  gases  expanding  under  constant  pressure, 
the  discordances  are  much  less,  and  may,  in  ordinary  circumstances, 
be  neglected.  Hence  gases  would  seem  to  be  indicated  by  nature  as 
the  proper  substances  by  which  to  measure  temperature,  if  differences 
of  temperature  are  to  be  measured  by  differences  of  volume. 

It  is  also  possible  to  establish  a  scale  of  temperature  by  assuming 
that  some  one  substance  rises  by  equal  increments  of  temperature  on 
receiving  successive  equal  additions  of  heat ;  in  other  words,  by  making 


ABSOLUTE   SCALE   OF  TEMPERATURE.  457 

some  one  substance  the  standard  of  reference  for  specific  heat,  and 
assuming  the  specific  heat  of  this  substance  to  be  the  same  at  all 
temperatures.  Here,  again,  the  scale  would  be  different  according  to 
the  liquid  chosen.  A  mixture  of  equal  weights  of  water  at  0°  C.  and 
100°  C.  will  not  have  precisely  the  same  temperature  as  a  mixture 
of  equal  weights  of  mercury  at  these  temperatures.  If,  however,  we 
resort  to  permanent  gases,  we  find  again  a  very  close  agreement,  so 
that,  if  one  gas  be  assumed  to  have  the  same  specific  heat  at  all  tem- 
peratures (whether  at  constant  volume  or  at  constant  pressure),  the 
specific  heat  of  any  other  permanent  gas  will  also  be  sensibly  in- 
dependent of  temperature.  More  than  this; — the  measurement  of 
temperature  by  assuming  the  specific  heats  of  permanent  gases  to 
be  constant,  agrees  almost  exactly  with  the  measurement  of  tem- 
perature by  the  expansion  of  permanent  gases.  For,  as  we  have 
seen  (§  3-47),  a  permanent  gas  under  constant  pressure  has  its  volume 
increased  by  equal  amounts  on  receiving  successive  equal  additions 
of  heat. 

The  air- thermometer,  or  gas-thermometer,  then,  has  a  greatly 
superior  claim  to  the  mercury  thermometer  to  be  considered  as  fur- 
nishing a  natural  standard  of  temperature. 

But  a  scale  which  is  not  only  sensibly  but  absolutely  independent 
of  the  peculiarities  of  particular  substances,  is  obtained  by  defining 
temperature  in  such  a  sense  as  to  make  appendix  (2)  to  the  second 
law  of  thermo-dynamics  rigorously  exact  According  to  this  system, 
the  ratio  of  any  two  temperatures  is  the  ratio  of  the  two  quantities 
of  heat  which  would  be  drawn  from  the  source  and  supplied  to  the 
refrigerator  by  a  completely  reversible  thermo-dynamic  engine  work- 
ing between  these  temperatures.  This  ratio  will  be  rigorously  the 
same,  whatever  the  working  substance  in  the  engine  may  be,  and 
whether  it  be  solid,  liquid,  or  gaseous. 

353  D.  Heat  required  for  Change  of  Volume  and  Temperature. — The 
amount  of  heat  which  must  be  imparted  to  a  body  to  enable  it  to 
pass  from  one  condition,  as  regards  volume  and  temperature,  to 
another,  is  not  a  definite  quantity,  but  depends  upon  the  course  by 
which  the  transition  is  effected.  It  is,  in  fact,  the  sum  of  two  quan- 
tities, one  of  them  being  the  heat  which  would  be  required  if  the 
transition  were  made  without  external  work — as  in  Joule's  experi- 
ment of  the  expansion  of  compressed  air  into  a  vacuous  vessel — and 
the  other  being  the  heat  equivalent  to  the  external  ^vorlc  which  the 
body  performs  in  making  the  transition.  As  regards  the  first  of 


458  THERMODYNAMICS. 

these  quantities,  its  amount,  in  the  case  of  permanent  gases,  depends 
almost  entirely  upon  the  difference  between  the  initial  and  final  tem- 
peratures, being  sensibly  independent  of  the  change  of  volume,  as 
Joule's  experiment  shows.  In  the  case  of  liquids  and  solids,  its 
amount  depends,  to  a  very  large  extent,  upon  the  change  of  volume, 
so  that,  if  the  expansion  which  heat  tends  to  produce  is  forcibly 
prevented,  the  quantity  of  heat  required  to  produce  a  given  rise  of 
temperature  is  greatly  diminished.  This  contrast  is  sometimes  ex- 
pressed by  saying  that  expansion  by  heat  involves  a  large  amount 
of  internal  work  in  the  case  of  liquids  arid  solids,  and  an  exceedingly 
small  amount  in  the  case  of  gases;  but  the  phrase  internal  work  has 
not  as  yet  acquired  any  very  precise  meaning. 

External  work  performed  against  uniform  hydrostatic  or  pneumatic 
pressure,  may  be  computed  by  'multiplying  the  increase  of  volume 
by  the  pressure  per  unit  area.  For,  if  we  suppose  the  expanding 
body  to  be  immersed  in  an  incompressible  fluid  without  weight,  con- 
fined in  a  cylinder  by  means  of  a  movable  piston  under  constant 
pressure,  the  work  done  by  the  expanding  body  will  be  spent  in 
driving  back  the  piston.  Let  A  be  the  area  of  the  piston,  x  the 
distance  it  is  pushed  back,  and  p  the  pressure  per  unit  area.  Then 
the  increment  of  volume  is  A  x,  and  the  work  done  is  the  product  of 
the  force  p  A  by  the  distance  x,  which  is  the  same  as  the  product  of 
p  by  Ax. 

As  an  illustration  of  the  different  courses  by  which  a  transition 
may  be  effected,  suppose  a  quantity  of  gas  initially  at  0°  C.  and  a 
pressure  of  one  atmosphere,  and  finally  at  100°  C.  and  the  same 
pressure,  the  final  volume  being  therefore  1-366  times  the  initial 
volume.  Of  the  innumerable  courses  by  which  the  transition  may 
be  made,  we  will  specify  two: — 

1st.  The  gas  may  be  raised,  at  its  initial  volume,  to  such  a  tem- 
perature that,  when  afterwards  allowed  to  expand  against  pressure 
gradually  diminishing  to  one  atmosphere,  it  falls  to  the  temperature 
100°  C.  Or, 

2d.  It  may  be  first  allowed  to  expand,  under  pressure  diminishing 
from  one  atmosphere  downwards,  until  its  final  volume  is  attained, 
and  may  then,  at  this  constant  volume,  be  heated  up  to  100°. 

In  both  cases  it  is  to  be  understood  that  no  heat  is  allowed  to 
enter  or  escape  during  expansion. 

Obviously,  the  first  course  implies  the  performance  of  a  greater 
amount  of  external  work  than  the  second,  and  it  will  require  the 


LOWERING  OF   FREEZING-POINT  BY  PRESSURE.  459 

communication  to  the  gas  of  a  greater  quantity  of  heat, — greater  by 
the  heat-equivalent  of  the  difference  of  works. 

When  a  body  passes  through  changes  which  end  by  leaving  it  in 
precisely  the  same  condition  in  which  it  was  at  first,  we  are  not 
entitled  to  assume  that  the  amounts  of  heat  which  have  entered  and 
quitted  it  are  equal.  They  are  not  equal  unless  the  algebraic  sum  of 
external  work  done  by  the  body  during  the  changes  amounts  to  zero. 
If  the  body  has  upon  the  whole  done  positive  work,  it  must  have 
taken  in  more  heat  than  it  has  given  out,  otherwise  there  would  be 
a  creation  of  energy;  and  if  it  has  upon  the  whole  done  negative 
work,  it  must  have  given  out  more  heat  than  it  has  taken  in,  other- 
wise there  would  be  a  destruction  of  energy.  In  either  case,  the 
difference  between  the  heat  taken  in  and  given  out  must  be  the 
equivalent  of  the  algebraic  sum  of  external  work. 

These  principles  are  illustrated  in  the  two  following  sections. 

353  E.  Lowering  of  Freezing-point  by  Pressure. — When  a  litre  (or 
cubic  decimetre)  of  water  is  frozen  under  atmospheric  pressure,  it 
forms  1  '087  of  a  litre  of  ice,  thus  performing  external  work  amount- 
ing to  '087x103  3=9  kilogramme-decimetres  ==  '9  of  a  kilogram- 
metre,  since  the  pressure  of  one  atmosphere  or  760  mm.  of  mercury 
is  103'3  kilogrammes  per  square  decimetre.  Under  a  pressure  of  n 
atmospheres,  the  work  done  would  be  '9  n  kilogrammetres,  neglecting 
the  very  slight  compression  due  to  the  increase  of  pressure.  If  the 
ice  is  allowed  to  melt  in  vacuo,  no  external  work  is  done  upon  it  in 
the  melting,  and  therefore,  in  the  whole  process,  at  the  end  of  which 
the  water  is  in  the  same  state  as  at  the  beginning,  heat  to  the 

'9  n 

amount  of  ^4  =  '0021 2  n  of  a  calorie  is  made  to  disappear.  This 
process  is  reversible,  for  the  water  might  be  frozen  in  vacuo  and 
melted  under  pressure;  and  hence,  by  appendix  (2)  to  the  second  law 
of  thermo-dynamics,  we  have 

•00212n     :     Q     ::     T-T"     :  T; 

where  Q  denotes  the  heat  taken  in  in  melting,  which  is  79 '25  calories, 
T  the  absolute  temperature  at  which  the  melting  occurs,  about  273°, 
and  T'  the  absolute  temperature  of  freezing  under  the  pressure  of  n 
atmospheres.  Hence  we  have 

•00212  n    :  79'25     :  :  T-T'     :  273; 
whence 

T-T'     =   -0073  n; 


4GO  THERMO-DYNAMICS. 

that  is,  the  freezing-point  is  lowered  by  '0073  of  a  degree  Cent,  for 
each  atmosphere  of  pressure. 

358  F.  Latent  Heat  at  Temperatures  below  the  Melting-point. — We 
have  seen  (§  231)  that  water  may  be  preserved  in  the  liquid  state  at 
temperatures  considerably  below  its  normal  freezing-point.  When 
ice  is  formed  at  these  low  temperatures,  the  latent  heat  absorbed 
must  be  less  than  70  25,  which  is  the  latent  heat  at  0°  C.  For, 
neglecting  the  trifling  amount  of  external  work  performed,  we  can 
assert  that  the  heat  lost  from  a  mass  of  water  at  0°,  in  its  passage  to 
ice  at  —t°,  is  independent  of  the  order  of  operations.  Now  the  specific 
heat  of  ice  is  '504,  that  of  water  being  1 ;  hence  the  heat  lost  in  making 
the  transition  in  the  ordinary  way  is  79  '25  +  '504  t,  while  that  lost 
by  first  cooling  down,  and  then  freezing  at  —t°  is  l  +  t,  I  denoting 
the  latent  heat  at  — 1°.  Equating  these  two  expressions,  we  have 
1  =  79-25  _  496  t. 

We  have  here  assumed  that  the  specific  heat  of  ice  is  -504  at  all 
temperatures.  Person's  experiments  seem  to  show  that  within  a 
degree  or  two  of  the  melting-point  it  has  a  much  larger  value. 

If  the  specific  heats  both  of  ice  and  water  were  constant  at  all 
temperatures,  we  might  determine  the  position  of  the  absolute  zero 
of  temperature  by  putting  1  =  0,  which  gives  —t°=  —160°  nearly,  a 
result  which  differs  widely  from  that  deduced  from  the  laws  of  gaseous 
expansion. 

Allowing  for  possible  variations  of  specific  heat  with  temperature, 
fche  expressions  for  the  heat  evolved  in  passing  from  water  at  0°  to 
ice  at  — 1°  are  79'25-f^s'  and  l  +  ts,  in  which  s  denotes  the  mean 
specific  heat  of  water  between  0°  and  —t0,  and  s'  the  mean  specific 
heat  of  ice  between  the  same  limits.  Equating  these  two  expressions, 

we  find 

1  =  79-25  -  t(s  -  s'). 

When  freezing  once  begins  at  a  temperature  below  0°,  it  proceeds 
very  rapidly,  accompanied  by  a  rise  of  temperature,  and  ceases  as 
soon  as  the  temperature  of  the  whole  mass  has  risen  to  0°.  To  com- 
pute the  proportions  of  ice  at  0°  and  water  at  0°  which  a  given  mass 
of  water  at  — 1°  will  yield,  we  may  reason  as  follows: — Calling  the 
whole  mass  unit}',  to  raise  it  from  its  initial  condition  to  0°,  and  then 
convert  a  fraction  m  of  it  into  ice  at  0°,  would  require  first  the  addition 
of  t  heat-units,  and  then  the  subtraction  of  79 '25m  heat-units,  that 
is  upon  the  whole  an  addition  of  t— 79'25  m.  Now  the  external  work 
being  inconsiderable,  the  amount  of  heat  required  from  without  for 


ANIMAL  HEAT  AND  WOEK.  461 

the  conversion  of  a  mass  1  of  water  at  — 1°  into  m  of  ice  at  0°  and 
l_m  of  water  at  0°,  will  be  independent  of  the  order  of  procedure; 
and  in  the  given  case  no  heat  is  added  from  without;  we  have 
therefore 

t-  79-25  m  =  0,    ^  =  ^25. 

359.  Animal  Heat  and  Work. — We  have  every  reason  to  believe 
that  animal  heat  and  motions  are  derived  from  the  energy  of  chemical 
combinations,  which  take  place  chiefly  in  the  act  of  respiration,  the 
most  important  being  the  combination  of  the  oxygen  of  the  air  with 
carbon  which  is  furnished  to  the  blood  Ivy  the  animal's  food.  The 
first  enunciation  of  this  view  has  been  ascribed  to  Lavoisier.  Rumford 
certainly  entertained  very  clear  and  correct  ideas  on  the  subject,  for 
he  says,  in  describing  his  experiments  on  the  boring  of  cannon : — 

"  Heat  may  thus  be  produced  merely  by  the  strength  of  a  horse, 
and,  in  a  case  of  necessity,  this  heat  might  be  used  in  cooking  vic- 
tuals. But  no  circumstances  could  be  imagined  in  which  this  method 
of  procuring  heat  would  be  advantageous;  for  more  heat  might  be 
obtained  by  using  the  fodder  necessary  for  the  support  of  a  horse  as 
fuel/' 

When  the  animal  is  at  rest,  the  heat  generated  by  chemical  com- 
bination is  equal  to  that  given  off  from  its  body ;  but  when  it  works, 
an  amount  of  heat  disappears  equivalent  to  the  mechanical  effect 
produced.  This  may  at  first  sight  appear  strange,  in  view  of  the 
fact  that  a  man  becomes  warmer  when  he  works.  The  reconciliation 
of  the  apparent  contradiction  is  to  be  found  in  the  circumstance  that, 
in  doing  work,  respiration  is  quickened,  and  a  greater  quantity  of 
carbon  consumed. 

Elaborate  experiments  on  this  subject  were  conducted  by  Hirn. 
He  inclosed  a  man  in  a  box  containing  a  tread -mill,  the  shaft  of  which 
passed  through  the  side  of  the  box;  and  the  arrangements  were  such 
that  the  man  could  either  drive  the  mill  against  external  resistance, 
by  continually  stepping  from  one  tread  to  the  next  above  in  the  usual 
way,  or  could  resist  the  motion  of  the  mill  when  driven  from  without, 
by  continually  descending  the  treads,  thus  doing  negative  work. 
Two  flexible  tubes  were  connected,  one  with  his  nostrils,  and  the 
other  with  his  mouth.  He  inhaled  through  the  former,  and  exhaled 
through  the  latter,  and  the  air  exhaled  was  collected  and  analyzed. 
The  heat  given  off  from  his  body  to  the  box  was  also  measured  with 
some  degree  of  approximation.  The  carbon,  exhaled,  and  heat  gene- 


462  THERMODYNAMICS. 

rated,  were  both  tolerably  constant  in  amount  when  the  man  was  at 
rest.  When  he  was  driving  the  mill  by  ascending  the  treads,  the 
heat  given  out  was  increased,  but  the  carbon  exhaled  was  increased 
in  a  much  greater  ratio.  When  he  was  doing  negative  work  by 
descending  the  treads,  the  heat  given  out,  though  less  in  absolute 
amount,  was  greater  in  proportion  to  the  carbon  exhaled,  than  in 
either  of  the  other  cases. 

360.  Heat  of  Chemical  Combination. — There  is  potential  energy 
between  the  particles  of  two  substances  which  would  combine  chemi- 
cally if  the  opportunity  were  afforded.     When  combination  actually 
takes  place,  this  potential  energy  runs  down  and  yields  an  equivalent 
of  heat.     We  may  suppose  that  the  particles  rush  together  in  virtue 
of  their  mutual  attraction,  and  thus  acquire  motions  which  constitute 
heat. 

In  every  case  of  decomposition,  an  amount  either  of  heat  or  some 
other  form  of  energy  must  be  consumed  equivalent  to  the  heat  of 
combination. 

360  A.  Vegetable  Growth. — In  the  growth  of  plants,  the  forces  of 
chemical  affinity  do  negative  work.  Particles  which  were  previously 
held  together  by  these  forces  are  separated,  and  potential  energy  is 
thus  obtained.  When,  wood  is  burned,  this  potential  energy  is  con- 
verted into  heat. 

We  are  not,  however,  to  suppose  that  plants,  any  more  than 
animals,  have  the  power  of  creating  energy.  The  forces  which  are 
peculiar  to  living  plants  are  merely  directive.  They  direct  the 
energy  of  the  solar  rays  to  spend  itself  in  separating  the  carbon  and 
oxygen  which  exist  united  in  the  carbonic  acid  of  the  air;  the  carbon 
being  taken  up  by  the  plant,  and  the  oxygen  left. 

Coal  is  the  remnant  of  vegetation  which  once  existed  on  the  earth. 
Thus  all  the  substances  which  we  are  in  the  habit  of  employing  as 
fuel,  are  indebted  to  the  sun  for  the  energy  which  they  give  out  as 
heat  in  their  combustion. 

361.  Solar  Heat. — The  amount  of  heat  radiated  from  the  sun  is 
great  almost  beyond  belief.     The  best  measures  of  it  have  been 
obtained  by  two  instruments  which  are  alike  in  principle — Sir  John 
Herschel's   actinometer   and    Pouillet's  pyrheliometer.      We   shall 
describe  the  latter,  which  is  represented  in  Fig.  314.     At  the  upper 
end,  next  the  sun,  is  a  shallow  cylinder  composed  of  very  thin  copper 
or  silver,  filled  with  water  in  which  the  bulb  of  a  thermometer  is 
inserted,  the  stem  being  partially  inclosed  in  the  hollow  tube  which 


SOLAR  HEAT. 


463 


supports  the  cylinder.     At  the  lov/er  end  of  the  tube  is  a  disc  equal 

and  parallel  to  the  base  of  the  cylinder.     This  is  intended  to  receive 

the  shadow  of  the  cylinder,  and  thus  assist 

the  operator  in  pointing  the  instrument 

directly  towards  the  sun.     The  cylinder  is 

blackened,  in  order  that  its  absorbing  power 

may  be  as  great  as  possible. 

The  instrument,  initially  at  the  tem- 
perature of  the  atmosphere,  is  first  placed 
for  five  minutes  in  a  position  where  it  is 
exposed  to  the  sky,  but  shaded  from  the 
sun,  and  the  increase  or  diminution  of  its 
temperature  is  observed ;  suppose  it  to  be 
a  fall  of  0°.  The  screen  which  shaded  it 
from  the  sun  is  then  withdrawn,  and  its 
rise  of  temperature  is  observed  for  five 
minutes  with  the  sun  shining  upon  it;  call 
this  rise  T°.  Finally,  it  is  again  screened 
from  the  sun,  and  its  fall  in  five  minutes  is 
noted  ; — call  this  0'°.  From  these  observa- 
tions it  is  inferred,  that  the  instrument, 

f\   .    f\r 

while  exposed  to  the  sun,  lost  — ^—  to  the 

air  and  surrounding  objects,   and   that   the  whole   heat  which  it 

f\   ,    f\r 

received  from  the  sun  was  T+  —£-,  or  rather  was  the  product  of 

this  difference  of  temperature  by  the  thermal  capacity  of  the 
cylinder  and  its  contents.  This  is  the  heat  which  actually  reaches 
the  instrument  from  the  sun,  but  a  large  additional  amount  has  been 
intercepted  by  absorption  in  the  atmosphere.  The  amount  of  this 
absorption  can  be  roughly  determined  by  comparing  observations 
taken  when  the  sun  has  different  altitudes,  and  when  the  distance 
traversed  in  the  air  is  accordingly  different.  Including  the  amount 
thus  absorbed,  Pouillet  computes  that  the  heat  sent  yearly  by  the  sun 
to  the  earth  would  be  sufficient  to  melt  a  layer  of  ice  30  metres  thick, 
spread  over  the  surf  ace  of  the  earth;  and  Sir  John  Herschel's  estimate 
is  not  very  different. 

The  earth  occupies  only  a  very  small  extent  in  space  as  viewed 
from  the  sun ;  and  if  we  take  into  account  the  radiation  in  all  direc- 
tions, the  whole  amount  of  heat  emitted  by  the  suri  will  be  found  to 
be  about  2100  million  times  that  received  by  the  earth,  or  sufficient 


Fig.  314.— Pyrheliometer. 


464  THERMODYNAMICS. 

to  melt  a  thickness  of  two-fifths  of  a  mile  of  ice  per  hour  over  the 
whole  surface^of  the  sun. 

361  A.  Sources  of  Solar  Heat. — The  only  causes  that  appear  at  all 
adequate  to  produce  such  an  enormous  effect,  are  the  energy  of  the 
celestial  motions,  and  the  potential  energy  of  solar  gravitation.  The 
motion  of  the  earth  in  its  orbit  is  at  the  rate  of  about  96,500  feet  per 
second.  The  kinetic  energy  of  a  pound  of  matter  moving  with  this 
velocity  is  equivalent  to  about  104,000  pound-degrees  Centigrade, 
whereas  a  pound  of  carbon  produces  by  its  combustion  only  8080. 
The  inferior  planets  travel  with  greater  velocity,  the  square  of  the 
velocity  being  inversely  as  the  distance  from  the  sun's  centre;  and 
the  energy  of  motion  is  proportional  to  the  square  of  velocity.  It 
follows  that  a  pound  of  matter  revolving  in  an  orbit  just  outside  the 
sun  would  have  kinetic  energy  about  220  times  greater  than  if  it 
travelled  with  the  earth.  If  this  motion  were  arrested  by  the  body 
plunging  into  the  sun,  the  heat  generated  would  be  about  2800  times 
greater  than  that  given  out  by  the  combustion  of  a  pound  of  charcoal. 
We  know  that  small  bodies  are  travelling  about  in  the  celestial 
spaces;  for  they  often  become  visible  to  us  as  meteors,  their  incan- 
descence being  due  to  the  heat  generated  by  their  friction  against 
the  earth's  atmosphere ;  and  there  is  reason  to  believe  that  bodies  of 
this  kind  compose  the  immense  circumsolar  nebula  called  the  zodiacal 
light,  and  also,  possibly,  the  solar  corona  which  becomes  visible  in 
total  eclipses.  It  is  probable  that  these  small  bodies,  being  retarded 
by  the  resistance  of  an  ethereal  medium,  which  is  too  rare  to  interfere 
sensibly  with  the  motion  of  such  large  bodies  as  the  planets,  are 
gradually  sucked  into  the  sun,  and  thus  furnish  some  contribution 
towards  the  maintenance  of  solar  heat.  But  the  perturbations  of  the 
inferior  planets  and  comets  furnish  an  approximate  indication  of  the 
quantity  of  matter  circulating  within  the  orbit  of  Mercury,  and  this 
quantity  is  found  to  be  such  that  the  heat  which  it  could  produce 
would  only  be  equivalent  to  a  few  centuries  of  solar  radiation. 

Helmholtz  has  suggested  that  the  smallness  of  the  sun's  density — 
only  J  of  that  of  the  earth — may  be  due  to  the  expanded  condition 
consequent  on  the  possession  of  a  very  high  temperature,  and  that 
this  high  temperature  may  be  kept  up  by  a  gradual  contraction. 
Contraction  involves  approach  towards  the  sun's  centre,  and  there- 
fore the  performance  of  work  by  solar  gravitation.  By  assuming 
that  the  work  thus  done  yields  an  equivalent  of  heat,  he  brings  out 
the  result  that,  if  the  sun  were  of  uniform  density  throughout,  the 


SOURCES   OF   ENERGY.  465 

heat  developed  by  a  contraction  amounting  to  only  one  ten-thousandth 
of  the  solar  diameter,  would  be  as  much  as  is  emitted  by  the  sun  in 
2100  years. 

361  B.  Sources  of  Energy  available  to  Man. — Man  cannot  produce 
energy;  he  can  only  apply  to  his  purposes  the  stores  of  energy  which 
he  finds  ready  to  his  hand.  With  some  unimportant  exceptions, 
these  can  all  be  traced  to  three  sources: — 

I.  The  solar  rays. 

II.  The  energy  of  the  earth's  rotation. 

III.  The  energy  of  the  relative  motions  of  the  inoon,  earth,  and 
sun,  combined  with  the  potential  energy  of  their  mutual  gravitation. 

The  fires  which  drive  our  steam-engines  owe  their  energy,  as  we 
have  seen,  to  the  solar  rays.  The  animals  which  work  for  us  derive 
their  energy  from  the  food  which  they  eat,  and  thus,  indirectly,  from 
the  solar  rays.  Our  water-mills  are  driven  by  the  descent  of  water, 
which  has  fallen  as  rain  from  the  clouds,  to  which  it  was  raised  in 
the  form  of  vapour  by  means  of  heat  derived  from  the  solar  rays. 

The  wind  which  propels  our  sailing-vessels,  and  turns  our  wind- 
mills, is  due  to  the  joint  action  of  heat  derived  from  the  sun,  and  the 
earth's  rotation. 

The  tides,  which  are  sometimes  employed  for  driving  mills,  are 
due  to  sources  II.  and  III.  combined. 

The  work  which  man  obtains,  by  his  own  appliances,  from  the 
winds  and  tides,  is  altogether  insignificant  when  compared  with  the 
work  done  by  these  agents  without  his  intervention,  this  work  being 
chiefly  spent  in  friction.  It  is  certain  that  all  the  work  which  they 
do,  involves  the  loss  of  so  much  energy  from  the  original  sources;  a 
loss  which  is  astronomically  insignificant  for  such  a  period  as  a  cen- 
tury, but  may  produce,  and  probably  has  produced,  very  sensible 
effects  in  long  ages.  In  the  case  of  tidal  friction,  great  part  of  the 
loss  must  fall  upon  the  energy  of  the  earth's  rotation;  but  the  case 
is  very  different  with  winds.  Neglecting  the  comparatively  insigni- 
ficant effect  of  aerial  tides,  due  to  the  gravitation  of  the  moon  and 
sun,  wind-friction  cannot  in  the  slightest  degree  affect  the  rate  of  the 
earth's  rotation,  for  it  is  impossible  for  any  action  exerted  between 
parts  of  a  system  to  alter  the  angular  momentum  of  the  system 
(53  F.)  The  effect  of  easterly  winds  in  checking  the  earth's  rota- 
tion must  therefore  be  exactly  balanced  by  the  effect  of  westerly 
winds  in  accelerating  it.  In  applying  this  principle,  it  is  to  be 
remembered  that  the  couple  exerted  by  the  wind  is  jointly  propor- 

30 


460  .      THERMODYNAMICS. 

tional  to  the  force  of  friction  resolved  in  an  easterly  or  westerly 
direction,  and  to  the  distance  from  the  earth's  axis. 

361  c.  Dissipation  of  Energy. — From  the  principles  laid  down  in  the 
present  chapter  it  appears  that,  although  mechanical  work  can  be 
entirely  spent  in  producing  its  equivalent  of  heat,  heat  cannot  be 
entirely  spent  in  producing  mechanical  work.  Along  with  the  con- 
version of  heat  into  mechanical  effect,  there  is  always  the  transference 
of  another  and  usually  much  larger  quantity  of  heat  from  a  body  at 
a  higher  to  another  at  a  lower  temperature.  In  conduction  and 
radiation  heat  passes  by  a  more  direct  process  from  a  warmer  to  a 
colder  body,  usually  without  yielding  any  work  at  all.  In  these 
cases,  though  there  is  no  loss  of  energy,  there  is  a  running  to  waste 
as  far  as  regards  convertibility ;  for  a  body  must  be  hotter  than 
neighbouring  bodies,  in  order  that  its  heat  may  be  available  for 
yielding  work.  This  process  of  running  down  to  less  available  forms 
has  been  variously  styled  diffusion,  degradation,  and  dissipation  of 
energy,  and  it  is  not  by  any  means  confined  to  heat.  We  can  assert 
of  energy  in  general  that  it  often  runs  down  from  a  higher  to  a 
lower  grade  (that  is  to  a  form  less  available  for  yielding  work),  and 
that,  if  a  quantity  of  energy  is  ever  raised  from  a  lower  to  a  higher 
grade,  it  is  only  in  virtue  of  the  degradation  of  another  quantity,  in 
such  sort  that  there  is  never  a  gain,  and  is  generally  a  loss,  of  avail- 
able energy. 

This  general  tendency  in  nature  was  first  pointed  out  by  Sir  W. 
Thomson.  It  obviously  leads  to  the  conclusion  that  the  earth  is 
gradually  approaching  a  condition  in  which  it  will  no  longer  be 
habitable  by  man  as  at  present  constituted. 


CHAPTER    XXXIII 


STEAM  AND  OTHER  HEAT  ENGINES. 


352.  Heat-engines. — The  name  of  heat-engine  or  thermo-dynamic 
engine  is  given  to  all  machines  which  yield  work  in  virtue  of  heat 
which  is  supplied  to  them.  Besides  the  steam-engine,  it  includes  the 
air-engine  and  the  gas-engine.  We  shall  first  describe  one  of  the 
best  forms  of  the  air-engine. 

363.  Stirling's  Air-engine. — Fig.  315  is  a  perspective  view,  and 
Fig.  3 1 6  a  section  of  the  engine  invented  by  Dr.  Robert  Stirling. 
The  particular  form  here  represented  is  that  which  has  been  adopted 
in  France  by  M.  Laubereau.  It  consists  of  two  cylinders  of  different 
diameters,  which  are  in  communication  with  each  other.  The  larger 
cylinder  is  divided  into  two  compartments  by  a  kind  of  large  piston 
made  of  plaster  of  Paris,  which,  however,  does  not  touch  the  sides  of 
the  cylinder,  and  thus  leaves  an  annular  space  for  communication 
between  the  two  compartments. 

The  bottom  of  the  large  cylinder,  which  is  directly  exposed  to  the 
action  of  the  furnace,  is  slightly  concave;  the  top  is  double,  thus 
affording  an  intermediate  space,  through  which  cold  water  is  kept 
circulating  by  means  of  a  pump  which  is  driven  by  the  machine. 
From  this  arrangement  it  follows  that,  when  the  mass  of  plaster  is 
at  the  bottom  of  the  cylinder,  it  will  intercept  the  heat  of  the  fire, 
being  a  very  bad  conductor,  and  thus  the  air  in  the  cylinder  will  be 
cooled  by  the  water  in  the  double  top.  On  the  other  hand,  when 
the  piston  is  in  contact  with  the  refrigerator,  the  air  will  be  exposed 
to  the  action  of  the  fire,  and  its  elastic  force  will,  consequently,  be 
increased. 

The  smaller  cylinder  is  open  above,  and  contains  a  piston  which 
drives  a  crank  on  the  axle  of  a  heavy  fly-wheel  of  cast-iron.  The  com- 
munication between  the  two  cylinders  is  in  the  lower  part  of  each. 


468 


STEAM   AND    OTHER   HEAT   ENGINES. 


Suppose  now  that  the  large  piston  is  in  contact  with  the  refrige- 
rator, while  the  small  piston  is  in  its  lowest  position.  The  air  is  thus 
exposed  to  the  action  of  heat,  expands,  and  raises  the  small  piston. 
If  we  now  suppose  the  large  piston  shifted  to  the  bottom  of  the 


Fig.  315.— Stirling's  Air-engine. 

cylinder,  the  air  will  cool,  and  its  tension  will  diminish,  becoming 
equal  to  or  even  less  than  that  of  the  atmosphere,  "the  small  piston 
will  thus  be  carried  to  the  bottom  of  the  cylinder  by  the  movement 
of  the  fly-wheel,  and  will  again  be  pushed  up  by  the  expanding 
air,  if  we  suppose  the  large  piston  to  rise  again  to  the  top  of  its 
cylinder. 


HISTORY   OF  THE   STEAM-ENGINE. 


469 


Fig.  316.— Section  of  Stirling's  Air-engine. 


This  motion  of  the  large  piston  is  effected,  as  shown  in  the  figure, 
by  means  of  an  eccentric  on  the  axle  of  the  fly-wheel.  The  engine 
is  of  small  size,  and  is  intended  for 
purposes  requiring  but  little  power. 
To  obtain  high  efficiency,  according 
to  the  principles  of  the  preceding 
chapter,  the  difference  of  tempera- 
ture between  the  two  ends  of  the 
large  cylinder  should  be  very  great. 
This  amounts  to  saying  that  the 
lower  end  must  be  kept  very  hot, 
since  it  is  practically  impossible  to 
keep  the  upper  end  much  cooler 
than  the  surrounding  atmosphere. 
The  facility  of  maintaining  a  very 
high  temperature  constitutes  at 
once  the  strength  and  the  weakness  of  the  air-engine.  The  bottom 
of  the  cylinder  becomes  rapidly  oxidized,  and  needs  frequent  renewal. 
Partly  for  this  reason,  and  partly  on  account  of  the  small  expansi- 
bility of  air  as  compared  with  the  expansion  which  takes  place  when 
water  is  converted  into  steam,  air-engines  are  seldom  employed  for 
high  powers. 

364.  The  Steam-engine :  its  History. — As  early  as  the  seventeenth 
century,  when  Otto  Guericke  and  Torricelli  were  investigating  the 
pressure  and  the  weight  of  air,  attention  had  been  given  to  the  phy- 
sical properties  of  steam,  and  the  idea  of  employing  it  as  a  source  of 
work  had  been  entertained. 

The  first  person  who  made  steam  drive  a  piston  was  Papin,  a  French 
philosopher,  inventor  of  the  digester  and  the  safety-valve  (born  1 650 ; 
died  1710).  About  the  year  1690  he  constructed  a  working  model, 
consisting  of  a  cylinder  open  at  the  top,  containing  a  piston  and  a 
little  water  below  it.  The  water  was  converted  into  steam  by  the 
application  of  heat,  and  raised  the  piston.  The  machine  being  then 
allowed  to  cool,  the  steam  lost  its  tension,  and  the  pressure  of  the 
atmosphere  forced  the  piston  to  descend.  A  backward  and  forward 
motion  was  thus  obtained,  which  Papin  proposed  to  convert  into  a 
rotatory  motion  by  means  of  rack1  and  pinion  work  and  ratchet-wheels. 


1  A  rack  is  a  straight  bar  with  teeth  at  one  edge,  which  works  with  a  toothed  wheel 
called  a  pinion. 


470  STEAM  AND   OTHER   HEAT   ENGINES. 

A  description  of  Papin's  machine  is  given  in  the  Acta  Eruditorum 
under  date  1690. 

The  first  steam-engine  actually  employed  for  doing  useful  work 
was  invented  by  Savery  about  1697,  and  was  extensively  used  for 
draining  mines.  Steam  from  a  separate  boiler  was  admitted  to  press 
upon  the  surface  of  water  in  a  vessel,  and  thus  force  it  up  through 
an  ascending  pipe;  and  on  the  condensation  of  the  steam,  water  from 
a  lower  level  was  raised  into  the  vessel  by  atmospheric  pressure. 
The  condensation  was  effected  by  applying  cold  water  to  the  outside 
of  the  vessel. 

Savery's  engine,  which  was  a  steam-pump,  and  not  an  engine 
adapted  for  general  purposes,  was  superseded  by  an  engine  jointly 
contrived  by  Newcomen,  Savery,  and  Cawley,  which  combined  the 
cylinder  and  piston  with  the  separate  boiler  and  with  condensation 
by  the  injection  of  cold  water  into  the  cylinder.  This  engine  is 
generally  referred  to  as  Newcomen's  atmospheric  engine, — so  called 
because  the  descent  of  the  piston  was  produced  by  atmospheric  pres- 
sure, on  the  condensation  of  the  steam  beneath  it. 

James  Watt  (born  1736;  died  1819),  who  effected  the  most  im- 
portant improvements  in  the  steam-engine,  had  his  attention  called 
to  the  subject  when  engaged  in  repairing  a  model  of  Newcomen's 
engine,  being  at  that  time  philosophical  instrument  maker  to  the 
University  of  Glasgow.  His  first  improvement  consisted  in  the 
introduction  of  a  separate  vessel  for  the  condensation  of  the  steam, 
so  as  to  allow  of  keeping  the  cylinder  always  hot. 

This  first  improvement,  which  immediately  produced  a  great  saving 
of  fuel,  was  followed  by  another  of  scarcely  less  importance.  This 
consisted  in  substituting  the  pressure  of  steam  for  the  atmospheric 
pressure,  which  in  Newcomen's  engine  caused  the  downward  stroke 
of  the  piston.  The  upward  stroke  was  effected  by  means  of  a  coun- 
terpoise, the  steam  being  admitted  to  press  equally  both  above  and 
below  the  piston.  These  two  improvements,  and  a  general  perfect- 
ing of  the  details  of  the  machinery,  caused  Watt's  engine  to  supersede 
that  of  Newcomen.  The  engine  thus  contrived  by  Watt  is  called 
single-acting,  because  only  the  down-stroke  of  the  piston  is  produced 
by  the  pressure  of  steam.  This  arrangement  is  particularly  adapted 
for  pumping,  and  is  commonly  employed  at  the  present  day  for 
draining  mines.  It  was  not  long  before  Watt  perfected  his  engine 
by  employing  steam  to  produce  both  the  up-stroke  and  the  down- 
stroke.  This  is  the  characteristic  of  the  double-acting  engine,  which 


THE   DOUBLE-ACTING   ENGINE. 


471 


was  carried  to  a  high  degree  of  perfection  by  the  inventor  himself, 
and  which  is  now  most  frequently  adopted  as  the  source  of  moving 
power.  We  may  add  that  the  improvements  introduced  in  the 
steam-engine  since  Watt's  time  have  been  matters  of  detail  rather 
than  of  principle.  We  proceed  to  describe  Watt's  engine. 

365.  Principle  of  the  Double-acting  Engine. — M  (Fig.  317)  is  a  boiler 
communicating  with  the  top  and  bottom  of  the  cylinder  by  means  of 
two  stop -cocks  a  and  b.  Connection  can  be  established  between  the 


Fig.  317.— Principle  of  the  Double-acting  Engine. 

cylinder  and  the  condenser  I  by  two  other  cocks  c  and  -d.  If  now 
the  cocks  a  and  c  are  opened,  and  b  and  d  shut,  the  steam  from  the 
boiler  will  arrive  above  the  piston  P,  while  that  which  was  previously 
introduced  below  will,  by  communication  with  the  condenser,  be 
more  or  less  condensed,  and  will  thus  lose  its  elastic  force;  the  piston 
will  accordingly  descend  to  the  bottom  of  the  cylinder.  The  two 
cocks  6  and  d  are  then  opened,  while  the  other  two  are  shut;  the 
steam  above  the  piston  is  thus  condensed,  while  that  below  the  piston 
forces  it  up,  thus  causing  the  upward  stroke,  after  which  the  piston 
may  again  be  made  to  descend,  and  so  on. 

We  thus  see  that,  by  suitable  manipulation  of  the  stop- cocks 
a,  6,  c,  d,  we  can  give  the  piston  a  backward  and  forward  motion,  which 
may  easily  be  transformed  into  one  of  rotation.  For  this  purpose 


472  STEAM   AND   OTHER   HEAT   ENGINES. 

the  piston-rod  is  connected  with  one  end  of  the  beam  EG  by  the 
jointed  parallelogram  CEDE,  while  the  other  end  of  the  beam  is 
jointed  to  the  connecting-rod  GL,  which  is  itself  jointed  to  the  crank 
of  the  fly-wheel  ER. 

It  will  be  seen  that,  if  the  piston  descends,  the  action  of  the  crank 
will  drive  the  wheel  in  the  direction  shown  by  the  arrow.  When 
the  piston  has  completed  its  downward  stroke,  the  connecting-rod 
and  the  crank  will  be  in  a  straight  line,  and  the  action  of  the  former 
upon  the  latter  will  have  no  tendency  to  turn  the  wheel  either  way. 
This  position  is  called  a  dead  point.  But  the  momentum  acquired 
by  the  fly-wheel  will  carry  it  past  this  position,  and,  the  piston  having 
then  commenced  its  upward  stroke,  the  rotatory  movement  will  con- 
tinue in  the  same  direction  until  the  rod  and  crank  are  at  the  other 
dead  point,  which  occurs  at  180°  from  the  first,  and  is  passed  over 
in  the  same  way.  We  thus  see  that,  by  means  of  the  alternate 
motion  of  the  piston,  we  can  obtain  a  rotatory  motion,  which  may 
be  imparted  to  a  horizontal  shaft,  and  made  to  drive  machinery  of 
any  kind. 

The  jointed  parallelogram  which  connects  the  piston-rod  with  the 
beam  is  one  of  the  most  ingenious  of  the  improvements  introduced 
by  Watt.  Its  use  is  evident.  When  the  engine  is  at  work,  the  end  E 
of  the  beam  describes  an  arc  of  a  circle,  while  the  end  D  of  the  piston- 
rod  moves  in  a  straight  line;  it  is  therefore  impossible  to  joint  them 
directly  together.  They  are  therefore  connected  through  the  medium 
of  the  short  rod  ED,  which,  with  the  two  other  rods,  BD  and  BC, 
together  with  the  part  CE  of  the  beam,  form  a  jointed  parallelo- 
gram; the  angles  of  which  can  vary  according  to  the  position  of  the 
beam.  The  angle  B  is  connected  by  a  joint  with  the  end  of  the 
radius-rod  BO,  movable  about  the  fixed  point  0.  The  effect  of  this 
arrangement  is  as  follows: — If  we  take  the  beam  in  a  horizontal 
position,  and  suppose  the  end  E  to  rise,  the  point  D  will  be  drawn 
towards  the  left  by  the  action  of  the  beam,  and  towards  the  right  by 
the  action  of  the  radius-rod  B  O,  which,  from  its  checking  the  move- 
ment of  the  piston-rod  to  either  side,  is  often  called  the  bridle-rod. 
It  will  easily  be  understood  that  these  two  contrary  actions  may  be 
made  to  balance  each  other  almost  exactly,  and  that,  accordingly, 
the  path  of  D  will  deviate  very  little  from  a  straight  line. 

366.  Arrangement  for  Admitting  the  Steam. — We  have  simplified 
the  description  of  the  steam-engine  by  supposing  that  the  cocks  a 
and  c,  b  and  d  were  alternately  opened  by  hand.  This,  however,  is 


THE   SLIDE-VALVE. 


473 


not  the  actual  arrangement,  the  opening  and  closing  of  the  passages 
being  really  effected  by  automatic  movements.  The  most  usual 
arrangement  for  this  purpose  is  the  slide-valve,  which  we  now  pro- 
ceed to  describe. 

The  steam,  instead  of  entering  the  cylinder  directly,  passes  into  it 
from  a  box  in  front  of  it  (Fig.  318),  which  is  called  the  valve-chest. 
In  the  opposite  face  of  the  box  from  that 
at  which  the  steam  enters,  are  three  holes 
or  ports  near  each  other.  The  uppermost 
of  these  communicates  with  the  upper 
part  of  the  cylinder;  the  lowest  one 
with  the  lower  part;  and  the  middle 
hole  with  o,  which  itself  is  in  communi- 
cation with  the  condenser.  Upon  this 
face  of  the  box  there  slides  a  rectan- 
gular piece  of  metal,  hollowed  out  on 
the  side  next  these  openings,  and  large 
enough  to  reach  over  two  of  the  ports 
at  once. 

In  the  right-hand  figure  this  slide-valve  is  supposed  to  be  at  the 
top  of  its  upward  stroke,  thus  admitting  the  steam  below  the  piston, 
and  pushing  it  in  the  direction  indicated  by  the  arrow ;  while  the 
steam  above  the  piston  is  put  in  communication  with  the  condenser. 
In  the  left-hand  figure,  the  opposite  position  is  shown ;  the  steam  is 
admitted  above  the  piston,  while  the  lower  part  of  the  cylinder  is  in 
communication  with  the  condenser. 

367.  Movement  of  the  Sliding-valve. — It  is  desirable  that  the  move- 
ment of  the  slide-valve  should  be  automatic;  for  this  purpose  the 
following  arrangement  is  employed.  A  circular  piece  of  metal  e, 


Fig.  318.— Slide-valve. 


Fig.  319. — Eccentric  for  moving  Slide-valve. 

called  the  eccentric,  is  traversed  by  the  shaft  of  the  engine  in  a  point 
which  is  not  the  centre  of  the  piece,  and  is  rigidly  attached  to  the 
shaft.  This  eccentric  is  surrounded  with  a  ring  of  metal,  which  can 


4-74?  STEAM   AND    OTHER   HEAT    ENGINES. 

turn  freely  about  it,  and  which  forms  part  of  the  triangular  frame  T. 
The  vertex  of  the  triangle  is  fastened  to  a  bent  lever  abc,  which  thus 
receives  an  oscillatory  movement  about  the  point  b.  This  movement 
raises  and  lowers  alternately  the  rod  d,  which  is  attached  to  the 
slidirig-valve,  and  thus  gives  that  valve  its  motion. 

368.  Air-pump  of  the  Condenser. — The  condenser  is  a  cylinder  into 
which  a  jet  of  cold  water  constantly  plays,  the  quantity  of  which 
can  be  increased  or  diminished  at  pleasure.     The  steam,  in  its  con- 
densation, heats  the  cold  water,  and  at  the  same  time  the  air  con- 
tained in  the  water  is  disengaged,  owing  to  the  small  pressure  in  the 
condenser.     It  is  thus  found  necessary  to  pump  out  both  the  air  and 
the  water ;  and  the  pump  which  does  this  is  driven  by  the  beam  of 
the  engine. 

The  warm  water  thus  drawn  out  is  conducted  to  a  reservoir,  whence 
a  portion  of  it  is  raised  by  a  second  pump,  and  forced  into  the  boiler. 
Finally,  a  third  pump,  usually  of  greater  power  than  the  other  two, 
raises  water  from  some  external  source,  and  discharges  it  into  a  bath 
called  the  cold  well,  which  feeds  the  condenser.  These  last  two  pumps 
are  also  connected  with  the  beam  of  the  engine. 

369.  Governor-balls. — The  apparatus  called  the  governor-balls  or 
the  centrifugal  governor  was  designed  by  Watt  for  the  purpose  of 
regulating  the  admission  of  steam  in  such  a  manner  as  to  render  the 
rate  of  the  engine  nearly  constant  through  all  variations  of  the  resist- 
ance to  be  overcome. 

It  consists  of  a  vertical  axis  y  (Fig.  320),  which  receives  a  rotatory 
movement  from  the  machine.  To  the  top  of  this  are  jointed  two 
rods  a/3,  a'/?',  carrying  the  heavy  balls  Z  and  Z'.  Two  other  rods, 
/3  e,  /3V,  are  jointed  to  the  first,  so  as  to  form  with  them  a  lozenge, 
the  lower  end  of  which  is  fastened  to  a  sliding-ring  m,  which  sur- 
rounds the  axis  of  rotation.  When  the  engine  is  at  rest,  the  sides  of 
the  lozenge  are  as  near  as  possible  to  the  vertical,  but  when  it  begins 
to  work,  the  balls  are  carried  out  from  the  vertical  by  centrifugal 
force,  and  the  distance  increases  with  the  velocity  of  rotation.  The 
sliding-ring  is  thus  raised,  and,  by  means  of  a  system  of  levers,  acts 
upon  a  throttle- valve  (a  disc  turning  about  a  diameter)  in  the  steam- 
pipe,  so  as  to  diminish  the  supply  of  steam  to  the  cylinder  when  the 
velocity  increases. 

370.  Use  -of  the  Fly-wheel. — From  the  mode  in  which  the  motion 
of  the  piston  is  transmitted  to  the  shaft,  it  is  obvious  that  the  driving 
couple  undergoes  great  variations  of  magnitude.     It  is  greatest  (con- 


WATT  S   ENGINE. 


475 


sidered  statically)  when  the  crank  is  nearly  at  right  angles  to  the 
connecting-rod,  and  diminishes  in  approaching  the  dead  points,  where 
it  vanishes  altogether.  These  variations  in  the  driving  couple  tend  to 
produce  corresponding  variations  in  the  velocity  of  rotation. 


Fig.  320.— WATT'S  ENGINE. 

ABCD,  jointed  parallelogram.  CC',  beam,  turning  about  O.  CXM,  connecting-rod.  O'M, 
crank,  attached  to  axis  of  fly-wheel.  V  V,  fly-wheel,  c,  eccentric,  which,  by  means  of  the  frame 
dd,  moves  the  lever  el,  which  moves  the  slide-valve,  xx,  an  endless  cord,  passing  over  a  pulley 
on  the  axis  0',  and  over  a  second  pulley  z,  whose  motion  is  transmitted  by  bevel-wheels  to  the 
axis  y  of  the  centrifugal  governor,  am,  a  rod  moved  by  the  ring  m,  and  transmitting  its  move- 
ment by  means  of  levers  to  the  throttle-valve.  H,  condenser.  RR,  cold  well,  t,  tube  through 
which  the  water  of  the  cold  well  under  atmospheric  pressure  flows  into  the  condenser.  E  E', 
cylinder  of  exhaust-pump.  P,  piston  of  ditto.  S,  valve.  X,  rod  of  the  pump  U  which  supplies 
the  cold  well.  R',  bath  which  receives  the  water  drawn  from  the  condenser.  Y,  rod  of  the  feed- 
pump W,  which  draws  water  from  R'  and  forces  it  into  the  boiler. 

Other  causes  also  contribute  to  produce  the  same  result,  especially 
the  variations  in  the  amount  of  resistance  to  be  overcome.     If,  for 


476  STEAM  AND   OTHER   HEAT  ENGINES. 

instance,  the  engine  drives  a  wheel  with  cams  which  raise  a  tilt- 
hammer,  when  the  hammer  falls  the  principal  resistance  is  removed, 
and  the  engine  immediately  begins  to  quicken  its  speed.  When  the 
hammer  is  caught  again  by  the  next  cam,  the  velocity  is  suddenly 
diminished,  and  so  on.  Similar  results,  though  not  of  so  marked  a 
character,  are  produced  in  engines  of  all  kinds.  These  sudden  changes 
of  velocity,  if  not  mitigated,  would  be  very  injurious  to  the  mechan- 
ism of  the  engine,  by  the  shocks  which  they  would  produce. 

The  use  of  the  fly-wheel  is  to  remedy  this  evil.  It  is  a  wheel  of 
considerable  size  and  weight  (the  weight  being  collected  as  much  as 
possible  at  the  rim),  and  receives  a  rotatory  movement  from  the 
engine.  If  the  driving  power  increases,  or  the  resistance  diminishes, 
all  the  moving  parts  of  the  engine  acquire  increased  velocities;  but 
the  greatest  part  of  the  additional  energy  of  motion  thus  generated 
goes  to  the  fly-wheel,  which  has  such  a  large  moment  of  inertia  that 
a  very  slight  change  in  its  angular  velocity  represents  a  large  amount 
of  energy  (§  53 G).  The  energy  thus  absorbed  by  the  fly-wheel  is 
restored  by  it  when  the  velocity  is  checked;  and  the  rotation  of  the 
shaft  is  thus  rendered  nearly  uniform  in  all  parts  of  the  stroke.  The 
size  of  the  fly-wheel  is  usually  made  such  that  the  difference  between 

the  greatest  and  least  velocities  shall  not  exceed  about  ^  of  the  mean 
velocity. 

371.  General  Description  of  Watt's  Engine. — The  explanations  above 
given  will  enable  the  reader  to  understand  the  general  arrangement 
of  Watt's  engine  as  represented  in  Fig.  320.     It  is  merely  necessary 
to  remark  that  the  slide-valve  is  slightly  different  from  that  described 
above,  but  the  modification  is  not  of  any  importance. 

372.  Working  Expansively. — Among  the  modifications  introduced 
since  Watt's  time,  we  must  notice  in  the  first  place  what  is  called 
expansive  working.1     When  the  piston  has  performed  a  part  of  its 
stroke,  the  steam  is  shut  off  (or  in  technical  phrase  cut  off)  from  the 
cylinder,  and  the  expansive  force  of  the  steam  already  admitted  is 
left  to  urge  the  piston  through  the  remainder  of  its  course.     By  this 
means  a  great  economy  of  steam  may  be  effected.     The  part  of  the 
stroke  at  which  the  cut-off  occurs  may  be  determined  at  pleasure. 
It  is  sometimes  at  half-stroke,  sometimes  at  quarter-stroke,  some- 
times at  one-fifth  of  stroke.     In  the  latter  case,  the  piston  describes 

1  This  was  one  of  Watt's  inventions,  but  it  has  been  much  more  fully  developed  in  recent 
times. 


UNIVERSITY  OF  CALIFORNIA 

477 


the  remaining  four-fifths  of  its  stroke  under  the  gradually  diminish- 
ing pressure  of  the  steam  which  entered  the  cylinder  during  the  first 
fifth  ;  and  the  work  done  during  these  four-fifths  is  so  much  work 
gained  by  working  expansively. 

373.  Modification  of  Slide-valve  for  Expansive  Working.  —  The  cut- 
ting-otF  of  the  steam  before  the  end  of  the  stroke  is  usually  effected 
by  the  contrivance  represented  in  Fig.  321  :  ad,  ad',  are  two  plates 
forming  part  of  the  slide-valve 

and  of  much  greater  width  than 
the  openings  L,  I/.  The  excess 
of  width  is  called  lap.  By  this 
arrangement  one  of  the  apertures 

is    kept    Closed    for   SOnie    time,    SO  Fig.  32L-Slide  -valve  for  Expansive  Working. 

that  the  steam  is  shut  off,  and 

acts  only  by  its  expansion.  The  expansion  increases  with  the  lap, 
but  not  in  simple  proportion,  as  equal  movements  of  the  slide-valve 
do  not  correspond  to  equal  movements  of  the  piston.  The  amount  of 
expansion  can  also  be  regulated  by  means  of  the  link-motion,  which 
will  be  described  in  §  390. 

374.  Compound  Engines.  —  This  is  the  name  given  to  engines  in 
which  the  steam  performs  the  greater  part  of  its  expansion  in  a  second 
cylinder,  of  much  larger  cross-section  than  the  first,  the  increased 
area  of  pressure  on  the  piston  serving  to  compensate  for  the  dimin- 
ished  intensity  of  pressure  which 

exists  in  the  latter  part  of  the  stroke, 
and  thus  to  produce  greater  steadi- 
ness of  driving-power.  Various  me- 
thods have  been  adopted  for  con- 
necting the  two  cylinders.  One 
arrangement  for  this  purpose  is  re- 
presented in  Fig.  322.  p  is  the 
smaller  piston,  working  in  the 

Smaller  Cylinder  A  BCD.       Pis    the         Fig.  322.—  Compound-cylinder  Arrangement. 

larger  piston,  working  in  the  larger 

cylinder  A'B'C'D'.  In  the  up-stroke,  the  passage  DA'  is  closed,  and 
CB'  is  open.  The  small  piston  is  forced  up  by  the  high-pressure 
steam  beneath,  while  the  steam  above  it,  instead  of  escaping  to  a 
condenser,  expands  into  the  large  cylinder,  and  there  raises  the 
piston  P,  the  upper  part  of  the  large  cylinder  being  connected  with 
the  condenser.  In  the  down-stroke,  the  passage  CB'  is  closed,  and 


478  STEAM   AND    OTHER   HEAT   ENGINES. 


is  open.  The  two  piston-rods  are  connected  with  the  same  end 
of  the  beam,  and  rise  and  fall  together.  The  distribution  of  the 
steam  is  effected  by  means  of  two  slide-valves,  each  governed  by  an 
eccentric. 

Compound  engines  have  been  adopted  for  some  lines  of  ocean- 
steamers,  where  it  is  of  primary  importance  to  obtain  as  much  work 
as  possible  from  a  limited  quantity  of  fuel.  Engineers  are,  however, 
divided  in  opinion  as  to  whether  any  advantage  attends  their  use. 

374A.  Surface  Condensation.  —  In  several  modern  engines,  the  con- 
denser consists  of  a  number  of  vertical  tubes  of  about  half  an  inch 
diameter,  connected  at  their  ends,  and  kept  cool  by  the  external 
contact  of  cold  water.  The  steam,  on  escaping  from  the  cylinder, 
enters  these  tubes  at  their  upper  ends,  and  becomes  condensed  in  its 
passage  through  them,  thus  yielding  distilled  water,  which  is  pumped 
back  to  feed  the  boiler.  The  same  water  can  thus  be  put  through 
the  engine  many  times  in  succession,  and  the  waste  which  occurs  is 
usually  repaired  by  adding  from  time  to  time  a  little  distilled  water 
prepared  by  a  separate  apparatus. 

375.  Classification  of  Steam-engines.  —  The  distinctions  which  exist 
between  different  kinds  of  stationary  engines  relate  either  to  the 
pressure  of  the  steam,  or  to  its  mode  of  action,  or  to  the  arrangement 
of  the  mechanism,  especially  as  regards  the  mode  in  which  the  move- 
ment of  the  piston  is  transmitted  to  the  rest  of  the  machinery. 

On  the  first  of  these  heads,  it  must  be  remarked  that  the  terms 
low-pressure  and  high-pressure  are  no  longer  equivalent  to  con- 
densing and  non-condensing  as  they  once  were,  and  merely  express 
differences  of  degree. 

When  the  pressures  employed  are  very  low  there  is  little  risk  of 
explosion  and  little  wear  and  tear;  but  the  engine  must  be  very  large 
in  proportion  to  its  power,  and  expansive  working  cannot  be  em- 
ployed. Low-pressure  engines  are  always  condensing,  though  the 
converse  is  not  true. 

With  regard  to  the  mode  of  action  of  the  steam,  engines  may  be 
classed  as  condensing  or  non-condensing,  as  expansive  or  non-expan- 
sive. Condensation  increases  the  quantity  of  work  obtainable  from 
a  given  consumption  of  fuel,  and  is  almost  always  employed  for 
stationary  engines  where  the  supply  of  water  is  abundant,  and  also 
for  marine  engines,  but  it  is  dispensed  with  in  locomotives  and 
agricultural  engines. 

Expansive  working  is  also  conducive  to  efficiency,  as  is  obvious 


HIGH-PRESSURE   ENGINE. 


479 


from  §  372.  Assuming  the  temperature  of  the  steam  to  remain  con- 
stant during  the  expansion,  the  following  table,  calculated  by  an 
application  of  Boyle's  law,  exhibits  the  relative  amounts  of  work 


Fig.  323. — High-pressure  Engine  with  Vertical  Cylinder,  working  Expansively  and  without 
Condensation. 

A,  steam-pipe  through  which  the  steam  arrives  from  the  boiler.  Z,  valve-chest.  B,  slide-valve. 
C,  cylinder.  G  G,  guides  fixed  to  the  cylinder  and  to  the  frame  of  the  engine  at  K  and  H.  E  P, 
connecting-rod.  J,  crank.  V  V,  fly-wheel.  L,  eccentric  governing  the  slide-valve.  N,  eccentric 
of  the  exhaust-pump  P.  D,  outlet  pipe  for  the  steam.  M,  lever  of  throttle-valve,  regulated  by 
centrifugal  governor. 


obtained  from  the  same  weight  of  steam  with  different  ranges  of 
expansion : — 


Work 
done. 


Fraction  of  the 
stroke  completed  before  the 
shutting-off  of  steam. 

i-o i-ooo 

•9 1-105 

•8 1-223 

•7 1-357 

•6  .  1-509 


Fraction  of  the 

stroke  completed  before  the  Work 

shutting-off  of  steam.  done. 

•5 1-693 

•4 1-916 

•3 2-201 

•2 2-609 

•1   .  .  3-302 


480  STEAM  AND   OTHER   HEAT   ENGINES. 

Expansive  working  is  often  combined  with  the  superheating  of 
steam,  that  is  to  say,  heating  the  steam  after  it  has  been  formed,  so 
as  to  raise  its  temperature  above  the  point  of  saturation.  This 
increases  the  difference  of  temperatures  to  which,  according  to  the 
second  law  of  thermo-dynamics,  the  maximum  efficiency  is  propor- 
tional ;  and  experience  has  shown  that  an  actual  increase  of  efficiency 
is  thus  obtained. 

376.  Form  and  Arrangement  of  the  Several  Parts. — As  regards  their 
mechanism,  the  arrangement  of  steam-engines  is  considerably  varied. 
In  stationary  condensing  engines,  the  beam  and  parallelogram  are 
usually  retained;    but  the  arrangement  of  high-pressure    non-con- 
densing engines  is  generally  simpler.      The  piston-rod  frequently 
travels  between  guides,  and  drives  the  crank  by  means  of  a  connect- 
ing-rod.    The  cylinder  may  be  either  vertical  or  horizontal,  or  even 
inclined  at  an  angle.     An  engine  of  this  kind  is  represented  in  Fig. 
323. 

Oscillating  Engines. — The  space  occupied  by  the  engine  may  be 
lessened  by  jointing  the  pistori-rod  directly  to  the  crank  without  any 
connecting-rod.  In  this  case  the  cylinder  oscillates  around  two 
gudgeons,  one  of  which  serves  to  admit  the  steam,  the  other  to  let 
it  escape.  The  distribution  of  the  steam  is  effected  by  means  of  a 
slide-valve  whose  movements  are  governed  by  those  of  the  cylinder. 
Oscillating  engines  are  very  common  in  steam-boats,  and  usually 
produce  an  exceedingly  smooth  motion. 

377.  Rotatory  Engines. — Numerous  attempts  have  been  made  to 
dispense  with  the  reciprocating  movement  of  a  piston,  and  obtain 
rotation  by  the  direct  action  of  steam.     Watt  himself  devised  an 
engine  on  this  plan  in  1782.     Hitherto,  however,  the  results  obtained 
by  this  method  have  not  been  encouraging.     Behren's  engine,  which 
we  now  proceed  to  describe,  is  one  of  the  most  promising  of  the 
rotatory  engines. 

Fig.  325  is  a  perspective  view  of  the  engine,  and  Fig.  326  a  cross- 
section  of  the  cylinders,  showing  the  mode  of  action  of  the  steam. 
C  and  C'  are  two  parallel  axes,  connected  outside  by  two  toothed 
wheels,  so  that  they  always  turn  in  opposite  directions.  One  of 
these  axes  is  the  driving-shaft  of  the  engine.  These  two  axes  are 
surrounded  by  fixed  collars  c  and  c',  which  fit  closely  to  the  cylin- 
drical sectors  E  and  E';  these  latter,  which  are  rigidly  connected  with 
the  axes  C,  C',  are  capable  of  moving  in  the  incomplete  cylinders 
A  and  A',  and  act  as  revolving  pistons.  In  the  position  represented 


ROTATORY   ENGINES. 


481 


in  the  figure,  the  steam  enters  at  B,  and  will  escape  at  D;  it  is  acting 
only  upon  the  sector  E,  and  pushes  it  in  the  direction  indicated  by 
the  arrow;  the  shaft  C  is  thus  turned,  and  causes  the  shaft  (7  to  turn 


Fig.  325.— Behren's  Rotatory  Engine. 


in  the  opposite  direction,  carrying  with  it  E',  to  which  it  is  attached. 
After  half  a  revolution  the  sector  E'will  be  in  a  position  correspond- 
ing, left  for  right,  to  that  which  E  now  occupies ;  it  will  then  be 
urged  by  the  steam,  so  as  to  continue  the  motion  in  the  same  direc- 

31 


482 


STEAM   AND   OTHER   HEAT   ENGINES. 


tion  for  another  half- re  volution,  when  the  two  sectors  will  have 
resumed  the  position  represented  in  the  figure. 

380.  Boilers. — There  are  many  forms  of  boiler  in  use.     That  which 

is  represented  in  Fig.  327  is  the 
favourite  form  in  France,  and  is  also 
extensively  used  in  this  country, 
where  it  is  called  the  French  boiler, 
or  the  cylindrical  boiler  with  heaters. 
The  main  boiler-shell  A  is  cylindrical 
with  hemispherical  ends.  BB  are 
two  cylindrical  tubes  called  heaters, 
of  the  same  length  as  the  main  shell, 
and  connected  with  it  by  vertical 
tubes  d,  d,  of  which  there  are  usually 
three  to  each  heater.  A  horizontal  brick  partition,  a  little  higher  than 
the  centres  of  the  heaters,  extends  along  their  whole  length;  and  a  ver- 
tical partition  runs  along  the  top  of  each  heater,  except  where  inter- 
rupted by  the  vertical  tubes.  The  flame  from  the  furnace  is  thus 
compelled  to  travel  in  the  first  instance  backwards,  beneath  the 


.    Fig.  326.— Section  of,  Behren's  Engine. 


Fig.  327.— Boiler  with  Heaters. 

heaters;  then  forwards,  through  the  intermediate  space  between  the 
heaters  the  vertical  tabes  and  the  main  shell;  and  lastly,  backwards, 
through  the  side  passages  CO,  which  lead  to  the  chimney.  By  thus 
compelling  the  flame  to  travel  for  a  long  distance  in  contact  with 
the  boiler,  the  quantity  of  heat  communicated  to  the  water  is 
increased. 

The  level  of  the  water  is  shown  at  A  in  the  left-hand  figure.     The 


SAFETY-VALVES.  483 

relative  spaces  allotted  to  the  steam  and  the  water  are  not  always 
the  same;  but  must  always  be  so  regulated  that  the  steam  shall 
arrive  in  the  cylinder  as  dry  as  possible,  that  is  to  say,  that  it  shall 
not  carry  with  it  drops  of  water.  Before  being  used,  boilers  should 
always  be  tested  by  subjecting  them  to  much  greater  pressures  than 
they  will  have  to  bear  in  actual  use.  Hydraulic  pressure  is  com- 
monly employed  for  this  purpose,  as  it  obviates  the  risk  of  explosion 
in  case  of  the  boiler  giving  way  under  the  test. 

381.  Boilers  with  the  Fire  Inside. — When  it  is  required  to  lessen 
the  weight  of  the  boiler,   without   much   diminishing  the  surface 

O  7  O 

exposed  to  heat,  as  in  the  case  of  marine  engines,  the  method  adopted 
is  to  place  the  furnace  inside  the  boiler,  so  that  it  shall  be  completely 
surrounded  with  water  except  in  front.  The  flame  passes  from  the 
furnace,  which  is  in  the  front  of  the  boiler,  into  one  or  two  large  tubes, 
leading  to  a  cavity  near  the  back,  whence  it  returns  through  a 
number  of  smaller  tubes  traversing  the  boiler,  and  finally  escapes  by 
the  chimney. 

382.  Bursting  of  Boilers:  Safety-valves. — Notwithstanding  the  tests 
to  which  boilers  are  subjected  before  being  used,  it  too  often  happens 
that,  owing  either  to  excessive  pressure  or  to  weakening  of  the  boiler, 
very  disastrous  explosions  occur. 

Excess  of  pressure  is  guarded  against  by  gauges,  which  show  what 
the  pressure  is  at  any  moment,  and  by  safety-valves,  which  allow 
steam  to  escape  whenever  the  pressure  exceeds  a  certain  limit. 

Various  kinds  of  manometer  or  pressure-gauge  have  been  described 
in  Chap.  xiv.  That  which  is  most  commonly  employed  in  connection 
with  steam-boilers  is  Bourdon's  (§  126). 

A  thermometer,  specially  protected  against  the  pressure  and  con- 
tact of  the  steam,  is  also  sometimes  employed,  under  the  name  of 
t/iermo-manometer,  on  the  principle  that  the  pressure  of  saturated 
steam  depends  only  on  its  temperature. 

The  safety-valve,  represented  in.  the  upper  part  of  Fig.  327,  consists 
of  a  piece  of  metal,  having  the  form  either  of  a  truncated  cone  or  of 
a  flat  plate,  fitting  very  truly  into  or  over  an  opening  in  the  boiler. 
The  valve  is  pressed  down  by  a  weighted  lever;  the  weight  and  the 
length  of  the  lever  being  calculated,  so  that  the  force  with  which  the 
valve  is  held  down  shall  be  exactly  equal  to  the  force  with  which  the 
steam  would  tend  to  raise  it  when  at  the  limiting  pressure.  In 
movable  engines,  the  weighted  lever  is  replaced  by  a  spring,  the 
tension  of  which  can  be  regulated  by  means  of  a  screw. 


4)84  STEAM   AND    OTHER   HEAT   ENGINES. 

Safety-valves  afford  ample  protection  against  the  danger  arising 
from  gradual  increase  of  pressure ;  but  they  are  liable  to  fail  in  cases 
where  there  is  a  sudden  generation  of  a  large  quantity  of  steam.  This 
explosive  generation  of  steam  may  occur  from  various  causes. 

If,  for  instance,  the  water  in  the  boiler  is  allowed  to  fall  too  low, 
the  sides  of  the  boiler  may  be  heated  to  so  high  a  temperature  that, 
when  fresh  water  is  admitted,  it  will  be  immediately  converted  into 
steam  on  coining  in  contact  with  the  metal. 

Hence  it  is  of  great  importance  to  provide  that  the  water  in  the 
boiler  shall  not  fall  below  a  certain  level,  depending  on  the  shape  of 
the  boiler  and  furnace. 

The  following  are  the  means  employed  for  securing  this  end: — 

1.  Two  cocks  are  placed,  one  a  little  below  the  level  at  which  the 
water  should  stand,  and  the  other  a  little  above  it;  these  are  opened 
from  time  to  time,  when  water  should  issue  from  the  first,  and  steam 
from  the  second. 

2.  The  water-gauge  is  a  strong  vertical  glass  tube,  having  its  ends 
fitted  into  two  short  tubes  of  metal,  proceeding  one  from  the  steam- 
space  and  the  other  from  the  water-space.     The  level  of  the  water  is 
therefore  the  same  in  the  gauge  as  in  the  boiler,  and  is  constantly 
visible  to  the  attendant.     The  metal  tubes  are  furnished  with  cocks, 
which  can  be  closed  if  the  glass  tube  is  accidentally  broken. 

384.  Causes  of  Explosion. — Another  cause  of  the  explosive  genera- 
tion of  steam  is  the  incrustation  of  the  boiler  with  a  hard  deposit, 
due  to  the  impurities  of  the  water  employed.  This  crust  is  a  bad 
conductor,  and  allows  the  portion  of  the  boiler  covered  with  it  to 
become  overheated;  when,  if  water  should  find  its  way  past  the  crust, 
and  come  in  contact  with  the  hot  metal,  there  is  great  danger  of 
explosion. 

The  best  preventive  of  incrustation  is  the  employment  of  distilled 
water  in  connection  with  surface  condensation  (§  374  A).  In  default 
of  this,  portions  of  the  water  in  the  boiler  must  be  blown  off  from 
time  to  time  so  as  to  prevent  it  from  becoming  too  highly  concen- 
trated. This  is  especially  necessary  when  the  boiler  is  fed  with  salt 
water. 

Among  the  causes  of  the  bursting  of  boilers,  we  may  also  notice 
undue  smallness  of  the  vertical  tubes  in  boilers  with  heaters  (§  380). 
When  this  fault  exists,  the  steam  which  is  generated  is  not  imme- 
diately replaced  by  water,  and  overheating  is  liable  to  occur. 

Another  cause  of  explosions  is  probably  to  be  found  in  a  property 


FEEDING   OF   THE   BOILER. 


485 


of  water  which  has  only  recently  been  recognized.  It  has  been 
shown  that,  when  water  is  deprived  of  air,  it  does  not  begin  boiling 
till  it  has  acquired  an  abnormally  high  temperature,  and  then  bursts 
into  steam  with  explosive  violence  (§  263,  Donny's  experiment). 
This  danger  is  to  be  apprehended  when  a  boiler,  which  has  been 
allowed  to  cool  after  being  for  some  time  in  use,  is  again  brought 
into  action  without  the  addition  of  a  fresh  supply  of  water. 

But  it  appears  that  the  most  frequent  cause  of  boiler  explosions  is 
the  gradual  eating  away  of  some  portion  of  the  boiler  by  rust,  so  as 
to  render  it  at  last  too  weak  to  withstand  the  pressure  of  the  steam 
within  it.  The  only  general  remedy  for  this  danger  is  periodical  and 
enforced  inspection. 

385.  Feeding  of  the  Boiler:  Giffard's  Injector.— The  feeding  of  the 
boiler  is  usually  effected  by  means  of  a  pump  driven  by  the  engine 


Fig.  328.— Giffard's  Injector. 

itself.  Of  late  years  this  plan  has  been  largely  superseded  by 
Giffard's  invention  of  an  apparatus  by  means  of  which  the  boiler  is 
supplied  with  water  by  the  direct  action  of  its  own  steam. 

This  very  curious  apparatus  contains  a  conical  tube  tt,  by  which 
the  steam  issues  when  the  injector  is  working;  the  steam  from  the 
boiler  comes  through  the  tube  VV,  and  enters  the  tube  tt  through 
email  holes  in  its  circumference.  On  issuing  from  the  cone  1 1,  the 


486  STEAM  AND   OTHER   HEAT   ENGINES. 

steam  enters  another  cone  c  c,  where  it  meets  the  water  which  is  to 
feed  the  boiler,  and  which  comes  through  the  tube  EE.  The  contact 
of  the  water  and  the  steam  produces  two  results :  (1)  the  steam,  which 
possesses  a  great  velocity  due  to  the  pressure  of  the  boiler,  communi- 
cates part  of  its  velocity  to  the  water;  (2)  at  the  same  time  the  steam 
is  condensed  by  the  low  temperature  of  the  water,  so  that  at  the 
extremity  of  the  cone  as  far  as  ee  the  entire  space  is  occupied  by 
water  only,  with  the  exception  of  a  few  bubbles  of  steam  which 
remain  in  the  centre  of  the  liquid  vein. 

The  liquid,  on  issuing  from  the  cone  cc,  traverses  an  open  space 
for  a  little  distance  before  entering  the  divergent  opposite  cone  d  d, 
through  which  it  is  conducted  to  the  boiler  by  the  pipe  M.  The 
water  will  not  enter  the  boiler  unless  it  possess  a  sufficient  velocity 
to  produce  in  the  divergent  cone  a  greater  pressure  than  that  which 
exists  in  the  boiler;  when  this  is  the  case,  the  excess  of  pressure  opens 
a  valve,  arid  water  enters  the  boiler  from  the  injector. 

We  may  complete  this  brief  description  by  pointing  out  one  or 
two  arrangements  by  which  the  action  of  the  apparatus  is  regulated. 
It  is  useful  to  be  able  to  vary  the  volume  of  steam  issuing  through 
the  cone  tt,  as  required  by  the  pressure  in  the  boiler;  this  is  easily 
effected  by  means  of  the  pointed  rod  a  a,  which  is  called  the  needle, 
and  is  screwed  forwards  or  backwards  by  turning  a  handle.  It  is 
also  necessary  to  be  able  to  regulate  the  volume  of  water  which  enters 
the  cone  c  c  from  the  supply-pipe  E ;  this  is  done  by  means  of  a  lever, 
which  is  not  shown  in  the  figure,  and  which  moves  the  tube  and 
cone  tt  forwards  or  backwards. 

The  tube  E  dips  into  a  bath  containing  the  feed-water;  and  AT 
is  the  overflow  pipe. 

It  appears  at  first  sight  paradoxical  that  steam  should  be  able,  as 
in  Giffard's  injector,  to  overcome  its  own  pressure,  and  force  water 
into  the  boiler  against  itself;  but  it  must  be  remembered  that  the 
water  which  is  forced  in  is  less  bulky  than  the  steam  which  issues, 
so  that  the  exchange,  though  it  produces  an  increase  of  mass  in  the 
contents  of  the  boiler,  involves  a  diminution  of  pressure,  as  well  as 
a  fall  of  temperature. 

388.  Locomotive:  History. — The  following  sketch  of  the  history  of 
the  locomotive  is  given  by  Professor  Rankine.1  "  The  application  of 
the  steam-engine  to  locomotion  on  land  was,  according  to  Watt,  sug- 

1  Manual  of  the  Steam- engine,  pp.  xxv-xxvn,  edition  1866. 


HISTORY   OF   THE   LOCOMOTIVE.  487 

gested  by  Robison  in  1759.  In  1784  Watt  patented  a  locomotive- 
engine,  which,  however,  he  never  executed.  About  the  same  time 
Murdoch,  assistant  to  Watt,  made  a  very  efficient  working  model  of 
a  locomotive-engine.  In  1802  Trevi thick  and  Vivian  patented  a 
locomotive-engine,  which  was  constructed  and  set  to  work  in  1804 
or  1805.  It  travelled  at  about  5  miles  an  hour,  with  a  net  load  of 
ten  tons.  The  use  of  fixed  steam-engines  to  drag  trains  on  railways 
by  ropes,  was  introduced  by  Cook  in  1808. 

"  After  various  inventors  had  long  exerted  their  ingenuity  in  vain 
to  give  the  locomotive-engine  a  firm  hold  of  the  track  by  means  of 
rack  work-rails  and  toothed  driving-wheels,  legs  and  feet,  and  other 
contrivances,  Blackett  and  Hedley,  in  1813,  made  the  important  dis- 
covery that  no  such  aids  are  required,  the  adhesion  between  smooth 
wheels  and  smooth  rails  being  sufficient.  To  adapt  the  locomotive- 
engine  to  the  great  and  widely- varied  speeds  at  which  it  now  has  to 
travel,  and  the  varied  loads  which  it  now  has  to  draw,  two  things 
are  essential — that  the  rate  of  combustion  of  the  fuel,  the  original 
source  of  the  power  of  the  engine,  shall  adjust  itself  to  the  work  which 
the  engine  has  to  perform,  and  shall,  when  required,  be  capable  of 
being  increased  to  many  times  the  rate  at  which  fuel  is  burned  in 
the  furnace  of  a  stationary  engine  of  the  same  size  ;  and  that  the 
surface  through  which  heat  is  communicated  from  the  burning  fuel 
to  the  water  shall  be  very  large  compared  with  the  bulk  of  th? 
boiler.  The  first  of  these  objects  is  attained  by  the  blast-pipe,  in- 
vented and  used  by  George  Stephenson  before  1825;  the  second  by 
the  tubular  boiler,  invented  about  1829,  simultaneously  by  Seguin 
in  France  and  Booth  in  England,  and  by  the  latter  suggested  to 
Stephenson.  On  the  6th  October,  1829,  occurred  that  famous  trial 
of  locomotive-engines,  when  the  prize  offered  by  the  directors  of  the 
Liverpool  and  Manchester  Railway  was  gained  by  Stephenson 's 
engine  the  'Rocket,'  the  parent  of  the  swift  and  powerful  locomo- 
tives of  the  present  day,  in  which  the  blast-pipe  and  tubular  boiler 
are  combined.  Since  that  time  the  locomotive  engine  has  been  varied 
and  improved  in  various  details,  and  by  various  engineers.  Its  weight 
now  ranges  from  five  tons  to  fifty  tons ;  its  load  from  fifty  to  five 
hundred  tons ;  its  speed  from  ten  miles  to  sixty  miles  an  hour." 

389.  Description  of  a  Locomotive. — A  section  of  a  locomotive  is 
represented  in  Fig.  329.  The  boiler  is  cylindrical.  Its  forward  end 
abuts  on  a  space  beneath  the  chimney,  called  the  smoke-box.  At  its 
other  end  is  a  larger  opening,  surrounded  above  and  on  the  two  sides 


488 


STEAM  AND   OTHER  HEAT   ENGINES. 


by  the  boiler,  and  called  the  fire-box.  The  fuel  is  heaped  up  on  the 
bars  which  form  the  bottom  of  the  fire-box,  and  the  cinders  fall  on 
the  line.  The  fire-box  and  smoke-box  are  connected  by  brass  tubes, 
firmly  rivetted  to  the  ends  of  the  boiler;  and  the  products  of  combus- 


Fig.  329. — Section  of  Locomotive,, 

tion  escape  by  traversing  these  from  end  to  end.  The  tubes  are  very 
numerous,  usually  from  150  to  180,  thus  affording  a  very  large  heat- 
ing surface.  The  water  in  the  boiler  stands  high  enough  to  cover  all 
the  tubes,  as  well  as  the  top  of  the  fire-box.  Its  level  is  indicated  in 
the  same  way  as  in  stationary  engines ;  and  water  is  pumped  in  from 
the  tender  as  required ;  its  amount  being  regulated  by  means  of  a 
stop- cock  in  the  pipe  e'. 

The  steam  escapes  from  the  boiler  by  ascending  into  a  dome,  which 
forms  its  highest  part,  and  thence  descending  the  tube  p,  this 
arrangement  being  adopted  in  order  to  free  the  steam  from  drops  of 
water.  It  then  passes  through  a  regulator  q,  which  can  be  opened 
to  a  greater  or  less  extent,  into  the  pipe  s,  which  leads  to  the  valve- 
chests  and  traverses  the  whole  length  of  the  boiler.  There  are  two 


APPARATUS   FOR   REVERSING   ENGINES. 


489 


cylinders,  one  on  each  side  of  the  engine,  each  having  a  valve-chest 
and  slide-valve,  by  means  of  which  steam  is  admitted  alternately 
before  and  behind  the  pistons.  The  steam  escapes  from  the  cylinder, 
through  the  blast-pipe  v,  up  the  chimney,  and  thus  increases  the 
draught  of  the  fire,  a  is  one  of  the  pistons,  b  the  piston-rod,  ccf  the 
connecting-rod,  which  is  jointed  to  the  crank  d  on  the  axle  of  the 
driving-wheel  m.  The  cranks  of  the  two  driving-wheels,  one  on  each 
side  of  the  engine,  are  set  at  right  angles  to  each  other,  so  that,  when 
one  is  at  a  dead  point,  the  other  is  in  the  most  advantageous  position. 
w  is  a  spring  safety-valve,  and  J  the  steam- whistle. 

390.  Apparatus  for  Reversing:  Link-motion. — The  method  usually 
employed    for   reversing   engines  is  known  as  Stephenson's  link- 


Fig.  330.— Link-motion. 

motion,  having  been  first  employed  in  locomotives  constructed  by 
Robert  Stephenson,  son  of  the  maker  of  the  "Rocket."  The  merit 
of  the  invention  belongs  to  one  or  both  of  two  workmen  in  his 
employ — Williams,  a  draughtsman,  who  first  designed  it,  and  Howe, 
a  pattern-maker,  who,  being  employed  by  Williams  to  construct  a 
model  of  his  invention,  introduced  some  important  improvements. 

The  link-motion,  which  is  represented  in  Fig.  330,  serves  two  pur- 
poses; first,  to  make  the  engine  travel  forwards  or  backwards  at 
pleasure ;  and,  secondly,  to  regulate  the  amount  of  expansion  which 


490  STEAM   AND  OTHER   HEAT   ENGINES. 

shall  take  place  in  the  cylinder.  Two  oppositely  placed  eccentrics, 
A  and  A',  have  their  connecting-rods  jointed  to  the  two  extremities 
of  the  link  B  B',  which  is  a  curved  bar,  having  a  slit,  of  uniform 
width,  extending  along  nearly  its  whole  length.  In  this  slit  travels 
a  stud  or  button  C,  forming  part  of  a  lever,  which  turns  about  a  fixed 
point  E.  The  end  D  of  the  lever  DE  is  jointed  to  the  connecting- 
rod  DN,  which  moves  the  rod  P  of  the  slide-valve.  The  link  itself 
is  connected  with  an  arrangement  of  rods  LI  KH,1  which  enables  the 
engine-driver  to  raise  or  lower  it  at  pleasure  by  means  of  the  handle 
GHF.  When  the  link  is  lowered  to  the  fullest  extent,  the  end  B 
of  the  connecting-rod,  driven  by  the  eccentric  A,  is  very  near  the 
runner  C  which  governs  the  movement  of  the  slide-valve;  this  valve, 
accordingly,  which  can  only  move  in  a  straight  line,  obeys  the  eccen- 
tric A  almost  exclusively.  When  the  link  is  raised  as  much  as  pos- 
sible, the  slide-valve  obeys  the  other  eccentric  A',  and  this  change 
reverses  the  engine.  When  the  link  is  exactly  midway  between  the 
two  extreme  positions,  the  slide-valve  is  influenced  by  both  eccen- 
trics equally,  and  consequently  remains  nearly  stationary  in  its 
middle  position,  so  that  no  steam  is  admitted  to  the  cylinder,  and 
the  engine  stops.  By  keeping  the  link  near  the  middle  position, 
steam  is  admitted  during  only  a  small  part  of  the  stroke,  and  con- 
sequently undergoes  large  expansion.  By  moving  it  nearer  to  one 
of  its  extreme  positions,  the  travel  of  the  slide-valve  is  increased,  the 
ports  are  opened  wider  and  kept  open  longer,  and  the  engine  will 
accordingly  be  driven  faster,  but  with  less  expansion  of  the  steam. 
As  a  means  of  regulating  expansion,  the  link-motion  is  far  from  per- 
fect, but  its  general  advantages  are  such  that  it  has  come  into  very 
extensive  use.  not  only  for  locomotives  but  for  all  engines  which  need 
reversal. 

393.  Gas-engines. — This  name  includes  engines  in  which  work  is 
obtained  by  the  expansion  of  a  mixture  of  coal-gas  and  air,  on  igni- 
tion or  explosion.  In  Lenoir's  engine  a  piston  is  driven  alternately 
in  opposite  directions  by  successive  ignitions  of  such  a  mixture  on 
opposite  sides  of  it,  the  proportions  of  gas  and  air  being  such  as  not 
to  yield  a  true  explosion. 

In  the  engine  of  Otto  and  Langen  (Fig.  331),  a  true  explosive 
mixture  is  introduced  beneath  the  piston,  and  is  exploded  by  means 

1 1  is  a  fixed  centre  of  motion,  and  the  rods  KI,  ML  are  rigidly  connected  at  right 
angles  to  each  other.  M  is  a  heavy  piece,  serving  to  counterpoise  the  link  and  eccentric 
rods. 


Fig.  331. — Gas-engine  of  Otto  and  Langcn. 


i92  STEAM   AND   OTHER   HEAT   ENGINES. 

of  a  lighted  jet,  which  is  brought  into  contact  with  the  mixture  by 
means  of  a  hole  in  a  movable  plate  of  metal,  driven  by  an  eccentric. 
The  upward  movement  of  the  piston  thus  produced  is  too  violent  to 
admit  of  being  directly  communicated  to  machinery.  The  piston-rod 
is  a  rack,  working  with  a  pinion,  which  is  so  mounted  that  it  can 
slip  round  on  the  shaft  when  the  piston  ascends,  but  carries  the  shaft 
with  it  when  it  turns  in  the  opposite  direction  during  the  descent  of 
the  piston,  this  descent  being  produced  by  the  pressure  of  the  atmo- 
sphere, as  the  steam  resulting  from  the  explosion  condenses,  and  the 
unexploded  gases  cool.  The  vessel  shown  on  the  right  contains  cold 
water,  which  is  employed  to  cool  the  cylinder  by  circulating  round 
the  lower  part  of  it.  The  quantity  of  water  required  for  this  purpose 
is  much  smaller,  and  the  consumption  of  gas  is  also  much  less,  than 
in  Lenoir's  engine. 


CHAPTER    XXXIV. 


TERRESTRIAL    TEMPERATURES. 


394.  Temperature  of  the  Air. — By  the  temperature  of  a  place 
meteorologists  commonly  understand  the  temperature  of  the  air  at 
a  moderate  distance  (5  or  10  feet)  from  the  ground.     This  element  is 
easily  determined  when  there  is  much  wind ;  but  in  calm  weather, 
and  especially  when  the  sun  is  shining  powerfully,  it  is  often  difficult 
to   avoid    the    disturbing    effect  of  radiation.      Thermometers   for 
observing  the  temperature  of  the  air  must  be  sheltered  from  rain 
and  sunshine,  but  exposed  to  a  free  circulation  of  air. 

395.  Mean  Temperature  of  a  Place. — The  mean  temperature  of  a 
day  is  obtained  by  making  numerous  observations  at  equal  intervals 
of  time  throughout  the  day  (24  hours),  and  dividing  the  sum  of  the 
observed  temperatures  by  their  number.     The  accuracy  of  the  deter- 
mination is  increased  by  increasing  the  number  of  observations;  as 
the  mean  temperature,  properly  speaking,  is  the  mean  of  an  infinite 
number  of  temperatures  observed  at  infinitely  short  intervals. 

If  the  curve  of  temperature  for  the  day  is  given,  temperature  being 
represented  by  height  of  the  curve  above  a  horizontal  datum  line, 
the  mean  temperature  is  the  height  of  a  horizontal  line  which  gives 
and  takes  equal  areas;  or  is  the  height  of  the  middle  point  of  any 
straight  line  (terminated  by  the  extreme  ordinates  of  the  curve) 
which  gives  and  takes  equal  areas. 

Attempts  have  been  made  to  lay  down  rules  for  computing  the 
mean  temperature  of  a  day  from  two,  three,  or  four  observations  at 
stated  hours;  but  such  rules  are  of  very  limited  application,  owing  to 
the  different  character  of  the  diurnal  variation  at  different  places ; 
and  at  best  they  cannot  pretend  to  give  the  temperature  of  an 
individual  day,  but  merely  results  which  are  correct  in  the  long  run. 
Observations  at  9  A.M.  and  9  P  M.  are  very  usual  in  this  country;  and 
the  half-sum  of  the  temperatures  at  these  hours  is  in  general  a  good 


494  TERRESTRIAL   TEMPERATURES. 

approximation  to  the  mean  temperature  of  the  day.  The  half-sum 
of  the  highest  and  the  lowest  temperature  in  the  day,  as  indicated 
by  maximum  and  minimum  thermometers,  is  often  adopted  as  the 
mean  temperature.  The  result  thus  obtained  is  usually  rather 
above  the  true  mean  temperature,  owing  to  the  circumstance  that 
the  extreme  heat  of  the  day  is  a  more  transient  phenomenon  than 
the  extreme  cold  of  the  night.  The  employment  of  self-registering 
thermometers  has,  however,  the  great  advantage  of  avoiding  errors 
arising  from  want  of  punctuality  in  the  observer.  The  correction 
which  is  to  be  added  or  subtracted  in  order  to  obtain  the  true  mean 
from  the  mean  of  two  observations  is  called  a  correction  for  diurnal 
range.  Its  amount  differs  for  different  places,  being  usually  greatest 
where  the  diurnal  range  itself  (§  113)  is  greatest. 

The  mean  temperature  of  a  calendar  month  is  computed  by 
adding  the  mean  temperatures  of  the  days  which  compose  it,  and 
dividing  by  their  number. 

The  mean  temperature  of  a  year  is  usually  computed  by  adding 
the  mean  temperatures  of  the  calendar  months,  and  dividing  by 
1 2 ;  but  this  process  is  not  quite  accurate,  inasmuch  as  the  calendar 
months  are  of  unequal  length.  A  more  accurate  result  is  obtained  by 
adding  the  mean  temperatures  of  all  the  days  in  the  year,  and 
dividing  by  365  (or  in  leap-year  by  366). 

398.  Isothermals. — The  distribution  of  temperature  over  a  large 
region  is  very  clearly  represented  by  drawing  upon  the  map  of  this 
region  a  series  of  isothermal  lines;  that  is,  lines  characterized  by  the 
property  that  all  places  on  the  same  line  have  the  same  temperature. 
These  lines  are  always  understood  to  refer  to  mean  annual  tempera- 
ture unless  the  contrary  is  stated  ;  but  isothermals  for  particular 
months,  especially  January  and  July,  are  frequently  traced,  one 
serving  to  show  the  distribution  of  temperature  in  winter,  and  the 
other  in  summer.  The  first  extensive  series  of  isothermals  was  drawn 
by  Humboldt  in  1817,  on  the  basis  of  a  large  number  of  observations 
collected  from  all  parts  of  the  world ;  and  the  additional  information 
which  has  since  been  collected  has  not  materially  altered  the  forms 
of  the  lines  traced  by  him  upon  the  terrestrial  globe.  They  are  in 
many  places  inclined  at  a  very  considerable  angle  to  the  parallels  of 
latitude ;  and  nowhere  is  this  deviation  from  parallelism  more  obser- 
vable than  in  the  neighbourhood  of  Great  Britain,  Norway,  and  Ice- 
land— places  in  this  region  having  the  same  mean  annual  temper- 
ature as  places  in  Asia  or  America  lying  from  1 0°  to  20°  further  south. 


INSULAR   AND   CONTINENTAL   CLIMATES. 


495 


399.  Insular  and  Continental  Climates. — The  difference  between 
the  temperatures  of  summer  and  winter  is  greatest  in  the  interior  of 
large  continents,  and  smallest  in  small  islands  in  the  midst  of  the 
ocean;  large  masses  of  water  being  exceedingly  slow  in  changing 
their  temperature,  and  powerfully  contributing  to  prevent  extremes 
of  temperature  from  occurring  in  their  neighbourhood.  It  is  common 
to  distinguish  in  this  sense  between  continental  climates  on  the  one 
hand  and  insular  or  marine  climates  on  the  other. 

Some  examples  of  both  kinds  are  given  in  the  following  table. 
The  temperatures  are  Centigrade : — 

MARINE  CLIMATES. 


Faroe  Islands,  .     .     . 
Isle  of  Unst  (Shetland), 
Isle  of  Man,      .     .     . 
Penzance,     .... 
Helston, 


Winter.                Summer.             Difference, 

3°-90 

IT-GO 

7°-70 

4  -05 

11  -92 

7  -87 

5  -59 

15  -03 

9  -49 

7  -04 

15  -83 

8  -79 

6  -19 

16  -00 

9  -81 

CONTINENTAL  CLIMATES. 


St  Petersburg 

-    8°70 

15°'96 

240-66 

Moscow,       

-10  '22 

17  -55 

27  -77 

-13  -66 

17  '35 

31  '01 

Slatoust 

16  '49 

16  '08 

32  '57 

Irkutsk                    .           ... 

-17  -88 

16  '00 

33  '88 

Jakoutsk,     

-38  -90 

17  -20 

56  -10 

400.  Temperature  of  the  Soil  at  Different  Depths.— By  employing 
thermometers  with  their  bulbs  buried  in  the  earth,  and  their  stems 
projecting  above,  numerous  observations  have  been  made  of  the 
temperature  from  day  to  day  at  different  depths  from  I  inch  to  2  or 
3  feet;  and  at  a  few  places  observations  of  the  same  kind  have  been 
made  by  means  of  gigantic  spirit-thermometers  with  exceedingly 
strong  bulbs,  at  depths  extending  to  about  25  feet.  It  is  found  that 
variations  depending  on  the  hour  of  the  day  are  scarcely  sensible  at 
the  depth  of  2  or  3  feet,  and  that  those  which  depend  on  the  time 
of  year  decrease  gradually  as  the  depth  increases,  but  still  remain 
sensible  at  the  depth  of  25  feet,  the  range  of  temperature  during  a 
year  at  this  depth  being  usually  about  2°  or  3°  Fahrenheit. 

It  is  also  found  that,  as  we  descend  from  the  surface,  the  seasons 
lag  more  and  more  behind  those  at  the  surface,  the  retardation  amount- 
ing usually  to  something  less  than  a  week  for  each  foot  of  descent; 
so  that,  at  the  depth  of  25  feet  in  these  latitudes,  the  lowest  tem- 
perature occurs  about  June,  and  the  highest  about  December. 

Theory  indicates  that  I  foot  of  descent  should  have  about  the  same 
effect  on  diurnal  variations  as  V3G5  that  is  19  feet  on  annual  varia- 


49  G  TERRESTRIAL   TEMPERATURES. 

tions ;  understanding  by  sameness  of  effect  equal  absolute  amounts  of 
lagging  and  equal  ratios  of  diminution. 

As  the  annual  range  at  the  surface  in  Great  Britain  is  usually  about 
3  times  greater  than  the  diurnal  range,  it  follows  that  the  diurnal 
range  at  the  depth  of  a  foot  should  be  about  one-third  of  the  annual 
range  at  the  depth  of  19  feet. 

The  variations  of  temperature  at  the  surface  are,  as  every  one 
knows,  of  a  very  irregular  kind;  so  that  the  curve  of  surface  tem- 
perature for  any  particular  year  is  full  of  sinuosities  depending  on 
the  accidents  of  that  year.  The  deeper  we  go,  the  more  regular  does 
the  curve  become,  and  the  more  nearly  does  it  approach  to  the  char- 
acter of  a  simple  curve  of  sines,  whose  equation  can  be  written 

y  =  a  sin.  x. 

Neglecting  the  departures  of  the  curve  from  this  simple  character, 
theory  indicates  that,  if  the  soil  be  uniform,  and  the  surface  plane, 
the  annual  range  (which  is  equal  to  2  a)  goes  on  diminishing  in  geo- 
metrical progression  as  the  depth  increases  in  arithmetical ;  and 
observation  shows  that,  if  10  feet  be  the  common  difference  of  depth, 
the  ratio  of  decrease  for  range  is  usually  about  J  or  J. 

To  find  a  range  of  a  tenth  of  a  degree  Fahrenheit,  we  must  go  to 
a  depth  of  from  50  to  80  feet  in  this  climate.  At  a  station  where 
the  surface  range  is  double  what  it  is  in  Great  Britain,  we  should 
find  a  range  of  about  two- tenths  of  a  degree  at  a  depth  and  in  a  soil 
which  would  here  give  one-tenth. 

These  remarks  show  that  the  phrase  "stratum  of  invariable  tem- 
perature," which  is  frequently  employed  to  denote  the  supposed  lower 
boundary  of  the  region  in  which  annual  range  is  sensible,  has  no 
precise  significance,  inasmuch  as  the  boundary  in  question  wrill  vary 
its  depth  according  to  the  sensitiveness  of  the  thermometer  employed. 

401.  Increase  of  Temperature  Downwards. — Observations  in  all 
parts  of  the  world  show  that  the  temperature  at  considerable  depths, 
such  as  are  attained  in  mining  and  boring,  is  much  above  the  surface 
temperature.  In  sinking  a  shaft  at  Rose  Bridge  Colliery,  near 
Wigan,  which  is  the  deepest  mine  in  Great  Britain,  the  temperature 
of  the  rock  was  found  to  be  94°  F.  at  the  depth  of  2440  feet.  In 
cutting  the  Mont  Cenis  tunnel,  the  temperature  of  the  deepest  part, 
with  5280  feet  of  rock  overhead,  was  found  to  be  about  85°  F. 

The  rate  of  increase  downwards  is  by  no  means  the  same  every- 
where; but  it  is  seldom  so  rapid  as  1°  F.  in  40  feet,  or  co  slow  as  1°  F. 
in  100  feet.  The  observations  at  Rose  Bridge  show  a  mean  rate  of 


TEMPERATURE  OF   SOIL.  497 

increase  of  about  1°  in  55  feet;  and  this  is  about  the  average  of  the 
results  obtained  at  other  places. 

This  state  of  things  implies  a  continual  escape  of  heat  from  the 
interior  of  the  earth  by  conduction,  and  the  amount  of  this  loss  per 
annum  can  be  approximately  calculated  from  the  absolute  values  of 
conductivity  of  rock  which  we  have  given  in  Chap.  xxx. 

There  can  be  no  reasonable  doubt  that  the  decrease  of  temperature 
upwards  extends  to  the  very  surface,  when  we  confine  our  attention 
to  mean  annual  temperatures,  for  all  the  heat  that  is  conducted  up 
through  a  stratum  at  any  given  depth  must  also  traverse  all  the 
strata  above  it,  and  heat  can  only  be  conducted  from  a  warmer  to  a 
colder  stratum.  Professor  Forbes  found,  at  his  three  stations  near 
Edinburgh,  increases  of  10<38,  00<96,  and  0°'19  F.  in  mean  temperature, 
in  descending  through  about  22  feet,  that  is,  from  the  depth  of  3  to 
the  depth  of  21  French  feet.  The  mean  annual  temperature  of  the 
surface  of  the  ground  is  in  Great  Britain  a  little  superior  to  that  of 
the  air  above  it,  so  far  as  present  observations  show.  The  excess 
appears  to  average  about  1°  F.  At  Trevandrum  in  India  the  excess 
is  in  the  same  direction,  and  amounts  to  5°  or  6°  F. 

402.  Decrease  of  Temperature  Upwards  in  the  Air. — In  comparing 
the  mean  temperatures  of  places  in  the  same  neighbourhood  at  dif- 
ferent altitudes,  it  is  found  that  temperature  diminishes  as  height 
increases,  the  rate  of  decrease  for  Great  Britain,  as  regards  mean 
annual  temperature,  being  about  1°  F.  for  every  300  feet.  A  decrease 
of  temperature  upwards  is  also  usually  experienced  in  balloon  ascents, 
and  numerous  observations  have  been  taken  for  the  purpose  of  deter- 
mining its  rate.  Mr.  Glaisher's  observations,  which  are  the  most 
numerous  as  well  as  the  most  recent,  show  that,  upon  the  whole,  the 
decrease  becomes  less  rapid  as  we  ascend  higher ;  also,  that  it  is  less 
rapid  with  a  cloudy  than  with  a  clear  sky.  The  following  table 
exhibits  a  few  of  Mr.  Glaisher's  averages : — 

Decrease  of  Temperature  Upwards. 

Height.  With  clear  sky.  With  cloudy  sky 

From  0  to  1000  feet,     ...      1°  F.  in  139  feet.  1°  F.  in  222  feet. 

From  0  to  10,000  ft.     ...      1°  F.  in  288  feet.  1°  F.  in  331  feet. 

From  0  to  20,000  ft.     ...      1°  F.  in  365  feet.  1°  F.  in  468  feet. 

These  rates  may  be  taken  as  representing  the  general  law  of  decrease 
which  prevails  in  the  air  over  Great  Britain  in  the  daytime  during 
the  summer  half  of  the  year ;  but  the  results  obtained  on  different 
days  differ  widely,  and  alternations  of  increase  and  decrease  are  by 
no  means  uncommon  in  passing  upwards  through  successive  strata 

of  air.      Still  more  recent  observations  by  Mr.  Glaisher,  relating 

32 


498  TERRESTRIAL   TEMPERATURES. 

chiefly  to  the  first  1000  feet  of  air,  show  that  the  law  varies  with  the 
hour  of  the  day.  The  decrease  upwards  is  most  rapid  soon  after 
midday,  and  is  at  this  time,  and  during  daytime  generally,  more 
rapid  as  the  height  is  less.  About  sunset  there  is  a  uniform  decrease 
at  all  heights  if  the  sky  is  clouded,  and  a  uniform  temperature  if  the 
sky  is  clear.  From  a  few  observations  which  have  been  taken  after 
sunset,  it  appears  that,  with  a  clear  sky,  there  is  an  increase  upwards 
at  night. 

That  an  extremely  low  temperature  exists  in  the  interplanetary 
spaces,  may  be  inferred  from  the  experimental  fact  recorded  by  Sir 
John  Herschel,  that  a  thermometer  with  its  bulb  in  the  focus  of  a 
reflector  of  sufficient  size  and  curvature  to  screen  it  from  lateral 
radiation,  falls  lower  when  the  axis  of  the  reflector  is  directed  upwards 
to  a  clear  sky  than  when  it  is  directed  either  to  a  cloud  or  to  the 
snow-clad  summits  of  the  Alps.  The  atmosphere  serves  as  a  protection 
against  radiation  to  these  cold  spaces,  and  it  is  not  surprising  that, 
as  we  increase  our  elevation,  and  thus  diminish  the  thickness  of  the 
coating  of  air  above  us,  the  protection  should  be  found  less  complete. 

403.  Cooling  of  an  Ascending  Column  of  Air. — Whenever  a  body 
of  air  ascends,  it  expands,  in  consequence  of  the  diminution  of  pres- 
sure ;  and  the  work  which  it  does  in  expanding  consumes  a  portion 
of  its  heat,  and  lowers  its  temperature.  In  like  manner,  when  air 
descends,  the  work  done  upon  it  in  compressing  it  raises  its  tempera- 
ture. The  amount  of  this  change  of  temperature  can  be  at  once 
inferred  from  §  347 A,  by  putting  t  =  1°  C.,  a.=  00366,  /3  =  -41.  In 
fact,  a  compression  or  expansion  amounting  to  '00366  of  the  volume 
which  the  air  would  occupy  at  zero,  alters  its  temperature  by  041°  C. 
Consequently,  for  an  alteration  of  1°  C.,  we  must  have  a  change  of 
volume  amounting  to  '00893,  which,  in  conjunction  with  the  change 
of  temperature,  implies  a  change  of  pressure  amounting  to  '00893  + 

•00366=: '0126=  gQ  of  the  actual  pressure.  This  corresponds  to  an 
ascent  or  descent  through  go  of  the  height  of  a  homogeneous  atmo- 
sphere (§  11 1  A),  that  is,  through  about  330  feet.  For  a  change  of 
1°  F.,  the  required  height  will  be  183  feet.  These  numbers  are  com- 
puted on  the  assumption  that  the  air  is  sufficiently  dry  to  behave  like 
a  permanent  gas.  If  ascending  air  contains  vapour  which  is  con- 
densed by  the  loss  of  heat,  this  condensation  greatly  retards  the  cool- 
ing ;  and  if  descending  air  contains  mist  which  is  dissipated  by  the 
gain  of  heat,  this  dissipation  retards  the  warming. 

It  is  obvious  that  the  ascent  of  warm  air  will  not  occur,  unless  the 


CAUSES   OF   WINDS.  4)99 

actual  decrease  of  temperature  upwards  is  more  rapid  than  the  cool- 
ing due  to  ascent ;  for  air  will  not  rise  if  the  process  of  rising  would 
make  it  colder  and  heavier  than  the  air  through  which  it  would  have 
to  pass. 

404.  Causes  of  Winds. — The  influences  which  modify  the  direction 
and  intensity  of  winds  are  so  various  and  complicated  that  anything 
like  a  complete  account  of  them  can  only  find  a  place  in  treatises 
specially  devoted  to  that  subject.    There  is,  however,  one  fundamental 
principle  which  suffices  to  explain  the  origin  of  many  well-known 
winds.     This  principle  is  plainly  illustrated  by  the  following  experi- 
ment, due  to  Franklin.     A  door  between  two  rooms,  one  heated,  and 
the  other  cold  (in  winter),  is  opened,  and  two  candles  are  placed,  one 
at  the  top,  and  the  other  at  the  bottom  of  the  doorway.     It  is  found 
that  the  flame  of  the  lower  candle  is  blown  towards  the  heated  room, 
and  that  of  the  upper  candle  away  from  it. 

From  this  experiment  we  can  deduce  the  following  general  prin- 
ciple:—  When  two  neighbouring  regions  are  at  different  tempera- 
tures, a  current  of  air  flows  from  the  warmer  to  the  colder  in  the 
upper  strata  of  the  atmosphere;  and  in  the  lower  strata  a  current 
flows  from  the  colder  to  the  warmer.  We  proceed  to  apply  this  prin- 
ciple to  the  land  and  sea  breezes,  the  monsoons,  and  the  trade- winds. 

405.  Land  and  Sea  Breezes. — At  the  sea-side  during  calm  weather 
a  wind  is  generally  observed  to  spring  up  at  about  eight  or  nine  in 
the  morning,  blowing  from  the  sea,  and  increasing  in  force  until  about 
two  or  three  in  the  afternoon.     It  then  begins  gradually  to  die  away, 
and  shortly  before  sunset  disappears  altogether.     A  few  hours  after- 
wards, a  wind  springs  up  in  the  opposite  direction,  and  lasts  till 
nearly  sunrise.     These  winds,  which  are  called  the  sea-breeze  and 
land-breeze,  are  exceedingly  regular  in  their  occurrence,  though  they 
may  sometimes  be  masked  by  other  winds  blowing  at  the  same  time. 
Their  origin  is  very  easily  explained.    During  the  day  the  land  grows 
warmer  than  the  water ;  hence  there  results  a  wind  blowing  towards 
the  warmer  region,  that  is,  towards  the  land.     During  the  night  the 
land  and  sea  both  grow  colder,  but  the  former  more  rapidly  than  the 
latter;  and,  accordingly,  the  relative  temperatures  of  the  two  elements 
being  now  reversed,  a  breeze  blowing  from  the  land  towards  the  sea 
is  the  consequence. 

Monsoons. — The  same  cause  which,  on  a  small  scale,  produces  the 
diurnal  alternation  of  land  and  sea  breezes,  produces,  on  a  larger  scale, 
the  annual  alternation  of  monsoons  in  the  Indian  Ocean,  and  the 
seasonal  winds  which  prevail  in  some  other  parts  of  the  world.  The 


500  TERRESTRIAL   TEMPERATURES. 

general  direction  of  these  winds  is  towards  continents  in  summer, 
and  away  from  them  in  winter. 

408.  Trade-winds:  General  Atmospheric  Circulation. — The  trade- 
winds  are  winds  which  blow  constantly  from  a  north- easterly  quarter 
over  a  zone  of  the  northern  hemisphere  extending  from  a  little  north 
of  the  tropic  of  Cancer  to  within  9  or  10  degrees  of  the  equator;  and 
from  a  south-easterly  quarter  over  a  zone  of  the  southern  hemisphere 
extending  from  about  the  tropic  of  Capricorn  to  the  equator.  Their 
limits  vary  slightly  according  to  the  time  of  year,  changing  in  the 
same  direction  as  the  sun's  declination.  Between  them  is  a  zone 
some  5°  or  6°  wide,  over  which  calms  and  variable  winds  prevail. 

The  cause  of  the  trade-winds  was  first  correctly  indicated  by 
Hadley.  The  greater  power  of  the  sun  over  the  equatorial  regions 
causes  a  continual  ascent  of  heated  air  from  them.  This  flows  over 
to  both  sides  in  the  upper  regions  of  the  atmosphere,  and  its  place  is 
supplied  by  colder  air  flowing  in  from  both  sides  below.  If  the 
earth  were  at  rest,  we  should  thus  have  a  north  wind  sweeping  over 
the  earth's  surface  on  the  northern  side  of  the  equatorial  regions,  and 
a  south  wind  on  the  southern  side.  But,  in  virtue  of  the  earth's 
rotation,  all  points  on  the  earth's  surface  are  moving  from  west  to 
east,  with  velocities  proportional  to  their  distances  from  the  earth's 
axis.  This  velocity  is  nothing  at  the  poles,  and  increases  in  approach- 
ing the  equator.  Hence,  if  a  body  on  the  earth's  surface,  and  origi- 
nally at  rest  relatively  to  the  earth,  be  urged  by  a  force  acting  along 
a  meridian,  it  will  not  move  along  a  meridian,  but  will  outrun  the 
earth,  or  fall  behind  it,  according  as  its  original  rotational  velocity 
was  greater  or  less  than  those  of  the  places  to  which  it  comes.  That 
is  to  say,  it  will  have  a  relative  motion  from  the  west  if  it  be  approach- 
ing the  pole,  and  from  the  east  if  it  be  approaching  the  equator. 

This  would  be  true,  even  if  the  body  merely  tended  to  keep  its 
original  rotational  velocity  unchanged,  and  the  reasoning  becomes 
still  more  forcible  when  we  apply  the  principle  of  conservation  of 
angular  momentum  (§§  53F,G),  in  virtue  of  which  the  body  tends 
to  increase1  its  absolute  rotational  velocity  in  approaching  the  pole, 
and  to  diminish  it  in  approaching  the  equator. 

Thus  the  currents  of  air  which  flow  in  from  both  sides  to  the 
equatorial  regions,  do  not  blow  from  due  north  and  due  south,  but 
from  north-east  and  south-east.  There  can  be  little  doubt  that,  not- 
withstanding the  variable  character  of  the  winds  in  the  temperate  and 
frigid  zones,  there  is,  upon  the  whole,  a  continual  interchange  of  air 

1  The  tendency  is  for  velocity  to  vary  inversely  as  distance  from  the  axis  of  rotation. 


GENERAL  ATMOSPHERIC   CIRCULATION. 


501 


between  them  and  the  intertropical  regions,  brought  about  by  the 
permanent  excess  of  temperature  of  the  latter.  Such  an  interchange, 
when  considered  in  conjunction  with  the  difference  in  the  rotational 
velocities  of  these  regions,  implies  that  the  mass  of  air  over  an  equa- 
torial zone  some  50°  or  60°  wide,  must,  upon  the  whole,  have  a  rela- 
tive motion  from  the  east  ;  and  that  the  mass  of  air  over  all  the  rest 
of  the  earth  must,  upon  the  whole,  have  a  relative  motion  from  the 
west.  This  theoretical  conclusion  is  corroborated  by  the  distribution 
of  barometric  pressure.  The  barometer  stands  highest  at  the  two 
parallels  which,  according  to  this  theory,  form  the  boundaries  between 
easterly  and  westerly  winds,  while  at  the  equator  and  poles  it  stands 
low.  This  difference  may  be  accounted  for  by  the  excess  of  centri- 
fugal force  possessed  by  west  winds,  and  the  defect  of  centrifugal  force 
in  east  winds.  If  the  air  simply  turned  with  the  earth,  centrifugal 
force  combined  with  gravity  would  not  tend  to  produce  accumulation 
of  air  over  any  particular  zone,  the  ellipticity  of  the  earth  being  pre- 
cisely adapted  to  an  equable  distribution.  But  if  a  body  of  air  or 
other  fluid  is  moving  with  sensibly  different  rotational  velocity  from 
the  earth,  the  difference  in  centrifugal  force  will  give  a  tendency  to 
move  towards  the  equator,  or  from  it,  according  as  the  differential 
motion  is  from  the  west  or  from  the  east.  The  easterly  winds  over 
the  equatorial  zone  should  therefore  tend  to  remove  air  from  the 
equator  and  heap  it  up  at  the  limiting  parallels  ;  and  the  westerly 
winds  over  the  remainder  of  the  earth  should  tend  to  draw  air  away 
from  the  poles  and  heap  it  up  at  the  same  limiting  parallels.  This 
theoretical  consequence  exactly  agrees  with  the  following  table  of 
mean  barometric  heights  in  different  zones  given  by  Maury:1  — 


North  Latitude.  Barometer. 

0°  to  5° 29-915 

5°  to  10° 29-922 

10°  to  15° 29-964 

15°  to  20° 30-018 

20°  to  25° 30-081 

25°  to  30° 30-149 

30°  to  35° 30-210 

35°  to  40° 30-124 

40°  to  45° 30-077 

45°  to  50° 30-060 

51°  29' 29-99 

59°  51' 29-88 

78°  37'     .    ,  ,  29759 


South  Latitude.  Barometer. 

0°to    5° 29-940 

5°  to  10° 29-981 

10°  to  15° 30-028 

15°  to  20° 30-060 

20°  to  25° 30-102 

25°  to  30° 30-095 

30°  to  36° 30-052 

42°  53' 29-90 

45°    0' 29-66 

49°    8' 29-47 

51°  33' 29-50 

54°  26' 29-35 

55°  52' 29-36 

60°    0' 29-11 

66°    0' 29-08 

74°    0'  ,  28-93 


Physical  Geography  and  Meteorology  of  the  Sea,  p.  180,  art.  362,  edition  1860. 


502  TERRESTRIAL   TEMPERATURES. 

This  table  shows  that  the  barometric  height  falls  off  regularly  on 
both  sides  from  the  two  limiting  zones  30°  to  35°  N.  and  20°  to  25°  S., 
the  fall  continuing  towards  both  poles  as  far  as  the  observations 
extend,  and  continuing  inwards  to  a  central  minimum  between  0° 
and  5°  N.1 

If  the  bottom  of  a  cylindrical  vessel  of  water  be  covered  with  saw- 
dust, and  the  water  made  to  rotate  by  stirring,  the  saw-dust  will  be 
drawn  away  from  the  edges,  and  heaped  up  in  the  middle,  thus 
showing  an  indraught  of  water  along  the  bottom  towards  the  region 
of  low  barometer  in  the  centre.  It  is  probable  that,  from  a  similar 
cause  (a  central  depression  due  to  centrifugal  force),  there  is  an 
indraught  of  air  along  the  earth's  surface  towards  the  poles,  under- 
neath the  primary  circulation  which  our  theory  supposes;  the  diminu- 
tion of  velocity  by  friction  against  the  earth,  rendering  the  lowest 
portion  of  the  air  obedient  to  this  indraught,  which  the  upper  strata 
are  enabled  to  resist  by  the  centrifugal  force  of  their  more  rapid 
motion.  This,  according  to  Professor  James  Thomson,2  is  the  ex- 
planation of  the  prevalence  of  south-west  winds  in  the  north  tem- 
perate zone ;  their  southerly  component  being  due  to  the  barometric 
indraught  and  their  westerly  component  to  differential  velocity  of 
rotation.  The  indraught  which  also  exists  from  the  limiting  parallels 
to  the  region  of  low  barometer  at  the  equator,  coincides  with  the 
current  due  to  difference  of  temperature ;  and  this  coincidence  may 
be  a  main  reason  of  the  constancy  of  the  trade- winds. 

406 A.  Origin  of  Cyclones. — In  the  northern  hemisphere  a  wind 
which  would  blow  towards  the  north  if  the  earth  were  at  rest,  does 
actually  blow  towards  the  north-east;  and  a  wind  which  would  blow 
towards  the  south  blows  towards  the  south-west.  In  both  cases,  the 
earth's  rotation  introduces  a  component  towards  the  right  with 
reference  to  a  person  travelling  with  the  wind.  In  the  southern 
hemisphere  it  introduces  a  component  towards  the  left. 

Again,  a  west  wind  has  an  excess  of  centrifugal  force  which  tends 
to  carry  it  towards  the  equator,  and  an  east  wind  has  a  tendency  to 
move  towards  the  pole;  so  that  here  again,  in  the  northern  hemi- 
sphere the  deviation  is  in  both  cases  to  the  right,  and  in  the  southern 
hemisphere  to  the  left. 

1  The  explanation  here  given  of  the  accumulation  of  air  towards  the  limiting  parallels, 
as  due  to  excess  and  defect  of  centrifugal  force,  appears  to  have,  been  first  published  by 
Mr.  W.  Ferrel,  a  gentleman  connected  with  the  American  Nautical  Almanack.  His  later 
treatise  (1860),  reprinted  from  vols.  i.  ii.  of  the  Mathematical  Monthly,  is  the  most  com- 
plete exposition  we  have  seen  of  the  theory  of  general  atmospheric  circulation. 

8  Brit.  Assoc.  Report,  1857. 


ANEMOMETERS. 


503 


We  Lave  thus  an  explanation  of  cyclonic  movements.  In  the 
northern  hemisphere,  if  a  sudden  diminution  of  pressure  occurs  over 
any  large  area,  the  air  all  round  for  a  considerable  distance  receives 
an  impetus  directed  towards  this  area.  But,  before  the  converging 
streams  can  meet,  they  undergo  deviation,  each  to  its  own  right,  so 
that,  instead  of  arriving  at  their  common  centre,  they  blow  tangen- 
tially  to  a  closed  curve  surrounding  it,  and  thus  produce  an  eddy 
from  right  to  left  with  respect  to  a  person  standing  in  the  centre. 
This  is  the  universal  direction  of  cyclonic  rotation  in  the  northern 
hemisphere;  and  the  opposite 
rule  holds  for  the  southern 
hemisphere.  The  former  is 
opposite  to,  the  latter  the 
same  as  the  direction  of  motion 
of  the  hands  of  a  watch  lying 
with  its  face  up.  In  each  case 
the  motion  is  opposite  to  the 
apparent  diurnal  motion  of  the 
sun  for  the  hemisphere  in  which 
it  occurs. 

407.  Anemometers. — Instru- 
ments for  measuring  either  the 
force  or  the  velocity  of  the  wind 
are  called  anemometers.  Its 
force  is  usually  measured  by 
Osier's  anemometer,  in  which 
the  pressure  of  the  wind  is 
received  upon  a  square  plate 
attached  to  one  end  of  a  spiral 
spring  (with  its  axis  horizon- 
tal), which  yields  more  or  less  according  to  the  force  of  the  wind, 
and  transmits  its  motion  to  a  pencil  which  leaves  a  trace  upon 
paper  moved  by  clock-work.  It  seems  that  the  force  received  by 
the  plate  is  not  rigorously  proportional  to  its  size,  and  that  a  plate 
a  yard  square  receives  rather  more  than  9  times  the  pressure 
of  a  plate  a  foot  square.  The  anemometer  which  has  yielded  the 
most  satisfactory  results  is  that  invented  by  the  Rev.  Dr.  Robinson 
of  Armagh,  which  is  represented  in  Fig.  331  A,  and  which  indicates 
the  velocity  of  the  wind.  It  consists  of  four  hemispherical  cups 
attached  to  the  ends  of  equal  horizontal  arms,  forming  a  horizontal 


Fig.  331  A. — Robinson's  Anemometer. 


504  TERRESTRIAL   TEMPERATURES. 

cross,  which  turns  freely  about  a  vertical  axis.  By  means  of  an  end- 
less screw  carried  by  the  axis,  a  train  of  wheel- work  is  set  in  motion; 
and  the  indication  is  given  by  a  hand  which  moves  round  a  dial;  or, 
in  some  instruments,  by  several  hands  moving  round  different  dials 
like  those  of  a  gas-meter.  The  anemometer  can  also  be  made  to 
leave  a  continuous  record  on  paper,  for  which  purpose  various  con- 
trivances have  been  successfully  employed.  It  was  calculated  by  the 
inventor,  and  confirmed  by  his  own  experiments  both  in  air  and 
water,  as  well  as  by  experiments  conducted  by  Prof.  C.  Piazzi  Smyth 
at  Edinburgh,  and  more  recently  by  the  astronomer-royal  at  Green- 
wich, that  the  centre  of  each  cup  moves  with  a  velocity  which  is 
almost  exactly  one-third  of  that  of  the  wind.  This  is  the  only  velo- 
city-anemometer whose  indications  are  exactly  proportional  to  the 
velocity  itself.  Dr.  Whewell's  anemometer,  which  resembles  a  small 
windmill,  is  very  far  from  fulfilling  this  condition,  its  variations  of 
velocity  being  much  less  than  those  of  the  wind. 

The  direction  of  the  wind,  as  indicated  by  a  vane,  can  also  be  made 
to  leave  a  continuous  record  by  various  contrivances;  one  of  the 
most  common  being  a  pinion  carried  by  the  shaft  of  the  vane,  and 
driving  a  rack  which  carries  a  pencil.  But  perhaps  the  neatest 
arrangement  for  this  purpose  is  a  large  screw  with  only  one  thread 
composed  of  a  metal  which  will  write  on  paper.  A  sheet  of  paper  is 
moved  by  clock-work  in  a  direction  perpendicular  to  the  axis  of  the 
screw,  and  is  pressed  against  the  thread,  touching  it  of  course  only 
in  one  point,  which  travels  parallel  to  the  axis  as  the  screw  turns, 
and  comes  back  to  its  original  place  after  one  revolution.  When  one 
end  of  the  thread  leaves  the  paper,  the  other  end  at  the  same  instant 
comes  on.  The  screw  turns  with  the  vane,  so  that  a  complete  revo- 
lution of  the  screw  corresponds  to  a  complete  revolution  of  the  wind. 
This  is  one  of  the  many  ingenious  contrivances  devised  and  executed 
by  Mr.  Beckley,  mechanical  assistant  in  Kew  Observatory. 


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Cloth.     Price,  $2.00. 

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be  reenforced  by  the  experience  of  every  intelligent  reader  of  its  too  brief  contents.1'—  The  Nation, 
July  24, 1879. 


A  Thousand  Flashes  of  French  Wit,  Wisdom,  and 
Wickedness, 

Collected  and  translated  by  J.  DE  FINOD.     One  vol.,  16mo.     Cloth.     Price,  $1.00. 
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is  needed  to  dispel  the  often  wellnigh  intolerable  languor  of  a  summer  afternoon."— Boston  Courier, 


D.  APPLETON  &  CO.'S  NEW  PUBLICATIONS.— (Continued.) 


The  Watering-Places  and  Mineral  Springs  of 
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With  Notes  on  Climatic  Resorts  and  Consumption,  Sanitariums,  Peat,  Mud, 
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FIFTH    AND     LAST    VOLUME     OF     THE     L.IFE     OF    THE    PRINCE 

CONSORT. 

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The  Fundamental  Concepts 


OF  MODERN  PHILOSOPHIC  THOUGHT,  CRITICALLY  AND  HISTORI- 
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An  Introduction  to  the  Study  of  Zoology.  By  Professor  T.  H.  HUXLEY,  F.  R.  S. 
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NOW  COMPLETE. 

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COOLE  Y'S 

Cyclopaedia  of  Practical  Beceipts, 

AND  COLLATERAL  INFORMATION  IN  THE 

Arts,  Manufactures,  Professions,  and  Trades,  including  Medicine, 
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prehensive Supplement  to  the  Pharmacopoeia,  and 
General  J3ook  of  Reference  for  the  Manu- 
facturer,   Tradesman,    Amateur, 
and  Heads  of  Families. 


SIXTH    EDITION.      Revised  and  partly  rewritten  by 

RICHARD  V.  TUSON, 

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Corr\plete  in  two  volurr\es,    8vo,    1,796  pages.      Witl\  Illustrations. 

Price,    $9.0O. 


COOLEY'S  CYCLOPJSDIA.  OF  RECEIPTS  lias  for  many  years  enjoyed  an  extended 
reputation  for  its  accuracy  and  comprehensiveness.  The  sixth  edition,  now  just 
completed,  is  larger  than  the  last  by  some  six  hundred  pages.  Much  greater 
space  than  hitherto  is  devoted  to  Hygiene  (including  sanitation,  the  composition 
and  adulteration  of  foods),  as  well  as  to  the  Arts,  Pharmacy,  Manufacturing 
Chemistry,  and  other  subjects  of  importance  to  those  for  whom  the  work  is  in- 
tended. The  articles  on  what  is  commonly  termed  "Household  Medicine  "  have 
been  amplified  and  numerically  increased. 

The  design  of  this  work  is  briefly  but  not  completely  expressed  in  its  title- 
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which  will  prove  invaluable  to  the  reader.  Lastly,  there  have  been  appended  to 
all  the  principal  articles  referred  to  brief  but  clear  directions  for  determining 
their  purity  and  commercial  value,  and  for  detecting  their  presence  and  propor- 
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PRIMERS 

IN  SCIENCE,    HISTORY,    AND    LITERATURE. 

18mo.         .         .         .         Flexible  cloth,  45  cents  each. 

SCIENCE    PRIMERS. 
Edited  by  Professors  HUXLEY,  ROSCOE,  and  BALFOUR  STEWART. 

Introductory T.  H.  HUXLEY. 

Chemistry. H.  E.  ROSCOE. 

Physics BALFOCR  STEWART. 

Physical  Geography * A.  GEIKIE. 

Geology A.  GEIKIE. 

Physiology M.  FOSTER. 

Astronomy . .  .  J.  N.  LOCKYER. 

Botany J.  D.  HOOKER. 

Logic W.  S.  JEVONS. 

Inventional  Geometry W.  G.  SPENCER. 

Pianoforte FRANKLIN  TAYLOR. 

Political  Economy .  .  .    W.  S.  JEVONS. 

Natural  Resources  of  the  United  States. .  .  .J.  H.  PATTON. 


HISTORY    PRIMERS. 

Edited  by  J.  E.  GREEN,  M.  A.,  Examiner  in  the  School  of  Modern  History  at  Oxford. 

Greece C.  A.  FYFFE. 

Rome M.  CREIGHTON. 

Europe E.  A.  FREEMAN. 

Old  Greek  Life J.  P.  MAHAFFY. 

Roman  Antiquities A.  S.  WILKINS. 

Geography GEORGE  GROVE. 


LITERATURE    PRIMERS. 
Edited  by  J.  R.  GREEN,  M.  A. 

English  Grammar R.  MORRIS. 

English  Literature,  new  edition,  with  supplement  containing  a  brief  history 

of  American  literature STOPFORD  A.  BROOKE. 

Philology J.  PEILE. 

Classical  Geography M.  F.  TOZER. 

Shakespeare E.  DOWDEN. 

Studies  in  Bryant J.  ALDEN. 

Greek  Literature R.  C.  JEBB. 

English  Grammar  Exercises R.  MORRIS. 

Homer W.  E.  GLADSTONE. 

English  Composition JOHN  NICHOL. 

(Others  in  preparation.} 

The  object  of  these  Primers  is  to  convey  information  in  such  a  manner  as  to  make  it 
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to  incline  them  to  more  systematic  after-studies.  The  woodcuts  which  illustrate  them 
embellish  and  explain  the  text  at  the  same  time. 

D.  APPLETON  &  CO.,  Publishers, 

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